---
abstract: 'Maintaining the ability to fire sparsely is crucial for information encoding in neural networks. Additionally, spiking homeostasis is vital for spiking neural networks with changing numbers of weights and neurons. We discuss a range of network stabilisation approaches, inspired by homeostatic synaptic plasticity mechanisms reported in the brain. These include weight scaling, and weight change as a function of the network’s spiking activity. We tested normalisation of the sum of weights for all neurons, and by neuron type. We examined how this approach affects firing rate and performance on clustering of time-series data in the form of moving geometric shapes. We found that neuron type-specific normalisation is a promising approach for preventing weight drift in spiking neural networks, thus enabling longer training cycles. It can be adapted for networks with architectural plasticity.'
author:
- |
    Katarzyna Kozdon$^{1}$, Peter Bentley$^{1,2}$\
    \
    $^1$University College London, London, United Kingdom\
    $^2$Braintree Ltd, London, United Kingdom\
    k.kozdon@cs.ucl.ac.uk
bibliography:
- 'references.bib'
title: 'Normalisation of Weights and Firing Rates in Spiking Neural Networks with Spike-Timing-Dependent Plasticity'
---

Introduction
============

Learning systems need to maintain a balance between plasticity and stability. In the brain, mechanisms such as long-term potentiation (LTP) and long-term depression (LTD) are vital for learning, but on their own they would lead to a powerful destabilisation of neuronal activity ([@Abbott2000; @Miller1994]). Strengthening of the synapses would lead to the increased likelihood of postsynaptic firing, whereas weakening of the synapses would lead to their silencing and eventually a cascade of further downstream changes in the same direction.

Similar problems are encountered in artificial intelligence. In unsupervised spiking neural networks (SNN) with spike-timing-dependent plasticity (STDP), weight drift is a known problem which impedes learning by leading to either weight silencing or saturation ([@Miller1994; @Abbott2000; @Oja1982]). In these networks, weight update is a function of the spike timing in a pair of connected neurons. Unlike in non-spiking supervised neural networks (NNN), the weight update is not aimed to minimise the loss function. Techniques such as L1 ([@RobertTibshirani1997]) and L2 ([@Nigam]) regularisation used to prevent excessive weight growth and parameter overfitting in NNN are not directly applicable to SNN, because of the complex relationship between the weights and spiking activity.

Additional difficulties arise when creating networks with plastic architecture. What value should be assigned to new weights, associated either with new synapses of existing neurons, or new neurons? The selected weight will not only affect the capacity of the new connection to learn, but will also cause downstream effects which are hard to predict in a complex systems, and may not be desirable. Thus, in order to utilise SNN for data processing, we need to identify methods preventing weight drift, silencing and saturation of spiking. Ideally, these methods should be applicable to SNN with changing numbers of neurons and synapses. These normalisation mechanisms cannot simply counteract the changes as it would effectively lead to erasing memories and undoing learning ([@Fox2017]).

One of the classical ways to tame Hebbian learning–induced bistability is the Bienenstock, Cooper and Munro model ([@Bienenstock1982]), according to which correlated spiking leads to LTP if the postsynaptic rate is higher than threshold, and to LTD if the firing rate is lower. The threshold changes as a function of average postsynaptic firing rate. However, there is no direct evidence that this mechanism exists in the brain.

Oja rule ([@Oja1982]) is another classical approach to stabilising networks with STDP. It extends Hebbian plasticity with scaling down synaptic efficacy as a function of the square of the firing rate.

Overall, models suggest that weight normalisation mechanisms are crucial for preserving the functionality of SNN. However, little research exploring and comparing different weight normalisation methods in applied SNN, and in SNN with plastic architecture, has been published.

The brain has developed homeostatic mechanisms for preserving its functionality while changing during development and learning. These mechanisms act both at the global ([@Turrigiano2008]) and local ([@Yu2009]) level. Four main forms have been distinguished ([@Fox2017]):

-   synaptic scaling (SS),

-   adjustment of the levels of inhibition and excitation,

-   basal firing rate homeostasis,

-   plasticity of the neuronal membrane properties.

Relevant to our project, it has been hypothesised that SS may be needed ”to ensure that firing rates do not become saturated during developmental changes in the number and strength of synaptic inputs, as well as stabilising synaptic strengths during Hebbian modification and facilitating competition between synapses" ([@Turrigiano1998]). Another attractive property of SS is stabilisation of neuronal activity without disrupting information storage and processing related to differences in synaptic strengths.

Model overview and experimental setup
=====================================

The model set-up is summarised in table \[table:norm\_setup\], and is a modification of [@Kozdon2018]. Briefly, we used the exponential leaky integrate-and-fire model ([@Barranca2014; @Fourcaud-Trocme2003]). Our network was composed of three feed-forward, fully-connected layers with 500, 50 and 10 neurons. 80% of the neurons were excitatory and 20% were inhibitory.

Our input data were bitmaps representing four different shapes (Fig. \[fig:EAInputs\]) moving in one of four directions at the speed of one pixel per frame. Each bitmap had 500 pixels, and each iteration of the network activity corresponded to a new frame.

We used evolutionary approach described in detail in [@Kozdon2018]. Clustering inputs by movement direction was used as a measure of fitness. A population of networks was initialised with random starting weights and learning hyperparameters. After training and testing, the top third of the networks were treated as non-sexually reproducing parents, each giving rise to three children: a child-clone, a child-clone which undergoes another training cycle, and a child with a mutation in one of the four learning parameters and exposed to another cycle of training.

We examined the spiking activity in each layer, and performance of the networks.

![Examples of bitmaps used as input data: a square, grid, ellipse and cross, each composed of 40 black pixels. One of the shapes was placed at a random location within the visual field (20 x 25 pixels) and moved up, down, left or right.[]{data-label="fig:EAInputs"}](EAInputs.png){width="45.00000%"}

Experimental setup: global weight normalisation
-----------------------------------------------

Normalisation was performed after each training epoch (10 frames of the input data). Based on our preliminary experiments, we selected the normalised sum of weights $w_{norm}$ to be tied to the number of all neurons ($n_n$) in the network and equal: $$w_{norm}= n_n \cdot 100
\label{eq:normalisedSumOfWeights}$$ We tested six set-ups:

1.  No normalisation. The weights were capped at 4 as in the previous paper ([@Kozdon2018]) (“control\_capped").

2.  No normalisation and weight-capping (“control").

3.  Normalisation with weight-capping (“norm\_capped").

4.  Normalisation without weight-capping (“norm").

5.  Separate normalisation for excitatory and inhibitory neurons, with weight-capping (“norm\_capped\_ie").

6.  Separate normalisation for excitatory and inhibitory neurons, without weight-capping. A proportion of $w_{norm}$ was assigned to each neuronal population; 80% was assigned to excitatory and 20% to inhibitory synapses (“norm\_ie").

We analysed a population of 12 networks over 20 generations. 10 repeats were performed. Significance was calculated using the Kruskal-Wallis test.

Results
=======

Global weight normalisation
---------------------------

Effects of normalisation were different depending on the presence of the weight cap \[fig:spiking\]).

In networks without normalisation but with weight-capping (“control\_capped"), spiking in the hidden and output layers (Fig. \[fig:spiking\] a and b) decreased with time. Networks without normalisation and weight-capping (“control") demonstrated a wide range of spiking patterns, and ranged from fully saturated to fully silent. Both of these un-normalised approached lead to activity patterns which are undesirable for information processing.

Networks with weight caps and normalisation (“norm\_capped" and “norm\_capped\_ie") demonstrated the most stable spiking behaviour, and were resistant to silencing while avoiding saturation during the examined period.

Networks with normalisation and capping (“norm\_capped"), and both set-ups with neuron type-specific weight normalisation (“norm\_capped\_ie" and “norm\_ie") were significantly more precise than the controls (Fig. \[fig:performance\]). Their performance also improved with time; normalisation with weight-capping had a lower precision than normalisation without the cap, but a steeper learning rate.

[0.45]{} ![Analysis of spiking activity. Median number of spikes per neuron per 50 iterations. Bars indicated standard deviation, and dots outliers.[]{data-label="fig:spiking"}](spike_count_plot_l2alife.png "fig:"){width="\textwidth"}

[0.45]{} ![Analysis of spiking activity. Median number of spikes per neuron per 50 iterations. Bars indicated standard deviation, and dots outliers.[]{data-label="fig:spiking"}](spike_count_plot_l3alife.png "fig:"){width="\textwidth"}

![Fitness of the networks. Double asterisk indicates significant difference between generation 0 and 19. Single asterisks indicate significant precision differences between normalised networks and their respective controls in generation 19. Bars indicate standard deviation.[]{data-label="fig:performance"}](fitness_dir.png){width="45.00000%"}

Discussion
==========

Our results demonstrate that even simple weight normalisation approaches can reduce saturation and silencing in SNN. These effects translated into improved performance on the unsupervised clustering tasks.

The simplest approach to network stabilisation is a global normalisation of the sum of weights, irrespective of the neuron type. The sum of weights is a function of the number of neurons, which gives it a potential to be suitable for networks with a changing number of neurons.

We also tested a neuron type-dependent modification of this approach, and normalised the sum of excitatory and inhibitory weights separately, assigning a proportion of the sum of weights to each population. This approach aimed to preserve the balance between the two. However, as the activity of each neuron depends on the strengths and types of all incoming weights, this is an indirect and global way of balancing excitation and inhibition, and does not normalise the exact balance between these two. This approach could be further extended to networks with multiple neuronal populations, even if the numbers of neurons fluctuate.

We are currently testing other approaches:

-   Normalisation of the spiking activity level:

    -   of the output neurons.

    -   of all neurons.

-   Activity-based adjustment of the level of inhibition and excitation.

When stabilising SNN, we primarily care about preserving their ability to encode information using spikes. Weight normalisation is an indirect approach to achieve this; a more direct approach would be to adjust the weights based on the spiking activity of the network. Spiking of the output layer is our direct readout. It is desired for the output neurons to fire sparsely (both activation of all neurons and total silence are to be avoided) so that multiple classes of input data can be encoded. Thus, we could focus solely on adjusting weights as a function of spiking in the output layer. This approach benefits from direct focus on stabilising our readout. However, spiking of the output layer may not provide enough resolution to fine-tune weights of the whole network. Alternatively, as the activity of the output layer is a function of the activity of the preceding layers, we could change the weights as a function of spiking of the whole network. This approach is less direct, but the breadth of observed behaviours may allow us to fine-tune the activity of the network.

Weight update can be multiplicative or additive. In the first case, weights are changed proportionally to their size. This method affects distribution of the weights. In additive weight update, a set amount $\Delta w$ is added or subtracted from each weight. Weights should not be allowed to drop below 0 to avoid switching between excitation and inhibition. This method allows to activate silent synapses.

Selective scaling of inhibitory and excitatory neurons as the function of spiking activity of the whole network or the output layer is a possible modification of this approach. If the number of spikes exceeds the permitted range, excitatory weights can be decreased and/or inhibitory increased; if spiking is below the permitted range, the reverse is executed. This approach can be adapted to minimise the weights without silencing of the network, and thus can be a form of activity-dependent mechanism reducing overfitting.

Conclusions
===========

Spiking neural networks with STDP require a mechanism for preventing weight drift. Our results show that even simple normalisation of the sum of weights, tied to the number of neurons provides stabilisation. Interestingly, the results are improved when normalisation was neuron type-specific, maintaining the sum of inhibitory and excitatory weights separately. This method is beneficial for maintaining trainable weights in networks with static architecture; it can also be implemented in networks with fluctuating number of neurons and weights, and with multiple neuronal populations, thus enabling their training and stabilisation of their activity levels.

Acknowledgements
================

This work was supported by Biotechnology and Biological Sciences Research Council and the London Interdisciplinary Biosciences Consortium.


Who said: “The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it... That is how we will preserve our planet, commanded to our care by God. Thats what will lend meaning to the creed our fathers once declared.”

By Gods mercy British and American science outpaced all German efforts. This revelation of the secrets of nature, long mercifully withheld from man, should arouse the most solemn reflections in the mind and conscience of every human being capable of comprehension. We must indeed pray that these awful agencies will be made to conduce to peace among the nations, and that instead of wreaking measureless havoc upon the entire globe, may become a perennial fountain of world prosperity.[Concerning use of the atomic bomb.]

Statement drafted by Churchill following the use of an atomic bomb on Hiroshima. Due to the change in government, the statement was released by Clement Attlee (6 Aug 1945). In Sir Winston Churchill, Victory: War Speeches by the Right Hon. Winston Churchill (1946), 289.

England was nothing, compared to continental nations until she had become commercial until about the middle of the last century, when a number of ingenious and inventive men, without apparent relation to each other, arose in various parts of the kingdom, succeeded in giving an immense impulse to all the branches of the national industry; the result of which has been a harvest of wealth and prosperity, perhaps without a parallel in the history of the world.

I came here to help make America more competitive and prosperous by developing an energy policy that increases conservation, promotes cleaner technologies, encourages development of renewables and enhances domestic production of gas and oil.

Man cannot have an effect on nature, cannot adopt any of her forces, if he does not know the natural laws in terms of measurement and numerical relations. Here also lies the strength of the national intelligence, which increases and decreases according to such knowledge. Knowledge and comprehension are the joy and justification of humanity; they are parts of the national wealth, often a replacement for the materials that nature has too sparcely dispensed. Those very people who are behind us in general industrial activity, in application and technical chemistry, in careful selection and processing of natural materials, such that regard for such enterprise does not permeate all classes, will inevitably decline in prosperity; all the more so were neighbouring states, in which science and the industrial arts have an active interrelationship, progress with youthful vigour.

Our civilization is an engineering civilization, and the prosperous life of the large population, which our earth now supports has become possible only by the work of the engineer. Engineering, however, is the application of science to the service of man, and so to-day science is the foundation, not only of our prosperity, but of our very existence, and thus necessarily has become the dominant power in our human society.

Problems in human engineering will receive during the coming years the same genius and attention which the nineteenth century gave to the more material forms of engineering.We have laid good foundations for industrial prosperity, now we want to assure the happiness and growth of the workers through vocational education, vocational guidance, and wisely managed employment departments. A great field for industrial experimentation and statemanship is opening up.

The expenditure [on building railways] of £286,000,000 by the people has secured to us the advantages of internal communication all but perfect,of progress in science and arts unexampled at any period of the history of the world,of national progress almost unchecked, and of prosperity and happiness increased beyond all precedent.

The future of humanity is uncertain, even in the most prosperous countries, and the quality of life deteriorates; and yet I believe that what is being discovered about the infinitely large and the infinitely small is sufficient to absolve this end of the century and millennium. What a very few are acquiring in knowledge of the physical world will perhaps cause this period not to be judged as a pure return to barbarism.

The Pacific coral reef, as a kind of oasis in a desert, can stand as an object lesson for man who must now learn that mutualism between autotrophic and heterotrophic components, and between producers and consumers in the societal realm, coupled with efficient recycling of materials and use of energy, are the keys to maintaining prosperity in a world of limited resources.

The progression of physical science is much more connected with your prosperity than is usually imagined. You owe to experimental philosophy some of the most important and peculiar of your advantages. It is not by foreign conquests chiefly that you are become great, but by a conquest of nature in your own country.

There are those who say we cannot afford to invest in science, that support for research is somehow a luxury at moments defined by necessities. I fundamentally disagree. Science is more essential for our prosperity, our security, our health, our environment, and our quality of life than it has ever been before. we can't allow our nation to fall behind. Unfortunately, that's exactly what's happened. Federal funding in the physical sciences as a portion of our gross domestic product has fallen by nearly half over the past quarter century. Time and again we've allowed the research and experimentation tax credit, which helps businesses grow and innovate, to lapse.

This is a moment to seize. The kaleidoscope has been shaken. The pieces are in flux. Soon they will settle again. Before they do, let us re-order this world around us. Today, humankind has the science and technology to destroy itself or to provide prosperity to all. Yet science cant make that choice for us. Only the moral power of a world acting as a community can.

We have before us the restoration of that ancient land whose name was a synonym for abundance, prosperity, and grandeur for many generations. Records as old as those of Egypt and as well attested tell of fertile lands and teeming populations, mighty kings and warriors, sages and wise men, over periods of thousands of years. ... A land such as this is worth resuscitating. Once we have apprehended the true cause of its present desolate and abandoned condition, we are on our way to restoring it to its ancient fertility. A land which so readily responded to ancient science, and gave a return which sufficed for the maintenance of a Persian Court in all its splendor, will surely respond to the efforts of modern science and return manifold the money and talent spent on its regeneration.

Without natural resources life itself is impossible. From birth to death, natural resources, transformed for human use, feed, clothe, shelter, and transport us. Upon them we depend for every material necessity, comfort, convenience, and protection in our lives. Without abundant resources prosperity is out of reach.

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan


Abstract

We describe the quantum transport of electrons by solitary waves and use it as the basis for a scheme for generating a single photon with highly nonclassical nature. A concave soliton acting as an attractive potential can capture an electron in its only eigenstate and the captured electron can be transported by soliton propagation. A single photon is generated by a transition between eigenstates in the interacting soliton potential when a soliton with a captured electron interacts with an empty soliton with a lower eigenstate.


Posts Tagged ‘style

It’s that time of the year again, a time to set our gaze on stars and starlets parading down the red carpet. If you’re hosting your own Oscar bash at your assigned Oscar-watching basecamp, make sure your outfit is Hollywood-worthy with the right ensemble.

The shoes are always a good place to start.

This year’s Oscars events call for the more than the little black dress, so don’t be afraid to sport some of the season’s hottest hues; dark purple, deep gold or dark green –

– and pair them up with these magnificent sandals:

Since it’s the season to show off that strut and really get noticed, enjoy a few moments of enchanting looks in these gorgeous Givenchy Sandals.They’re magical, bewitching and definitely something out of the ordinary; the criss-cross strapped booties are designed with a lace upper and leather lining, and your 3 ½” heel gives you a chance to enjoy a stiletto-like presence.

They’re the party heels of the season, and you can don them with any knee-length or mini-dress for Oscar night or beyond.

Golden Globes, Oscar Night, the Emmy’s…who cares?This year’s must-dress-up-for event is Inauguration Night, and the First Lady isn’t the only one with an excuse to dress up for the occasion.

Stylelist reports that A-listers are preparing for this years event by reserving designer gowns and ensembles worthy of their own award.Designers Kenneth Cole, Marc Jacobs and Sean John have been plenty busy sketching up wardrobe options for the dapper President-to-be, but what’s in store for the ladies at the ball?

This year’s top trends for the festivities include black and navy ensembles with streamlined silhouettes, bold red accessories, and ‘50s inspired dresses and skirts.

Just think of ways to incorporate red, white and blue into your ensemble. As we head to the shoe aisle, it’s no surprise that stilettos will reign supreme, and with Spring right around the corner, you can even get away with an open toe.

These serpentine heels from LAMB may just be the reason to show off those gams for the grand event; the 4” stacked stiletto heel sits atop a comfy ¾” platform and is designed with criss-cross straps with a sexy twist.It’s a perfect match for crashing the nearest inauguration party with your stiletto-loving self, or just for throwing a bash of your own as the hostess with the enviable shoes.

Stand tall and proud during the inaugural address and look forward to toasting to the event for history in the making – all while enjoying a few minutes under the spotlight.

When the weather outside is frightful – and those dreary days ahead call for the ol’ online shoe shopping spree – don’t let the latest lineup of cone heels pass you by. It’s the year’s latest trend that gives you a stylish, I-just-got-off-the-Milan-runways look.

A blend of geometric design and up-to-there heights, these heels are designed for a high impact presence.

Besides, why would you for a season of ankle booties and knee-high boots that compromise the chance to show off the overpriced manicure? It’s not easy to find peep-toe pumps that work for the chilly season ahead, but a girl’s got to find a way to prevent hiding toes behind thick socks all season.

I present to you, the Costume National leather pump, a cone-heeled number made with rich brown leather and an extra-high arch. It’s the 5” heel for those who can’t fathom stepping into stilettos for the night on the town, or for those who want to show off their playful side during the mid-week slump at the office. Plus, it works as the ultimate trade-out shoe after work – the perfect pair for those last minute dates where running home to change just isn’t possible. Tuck these inside your Morning After bag and you’ll have plenty of ammo to turn a few heads for the evening. The cone heel gives you extra support, carves out those calves, and delivers that extra height you need to show off those Gisele-like legs. Practice your trot, ladies because this one’s worth the challenge.

So as you’re slathering on the bronzer to keep up that sun-kissed glow, and trotting off to that date or shopping conquest that demands a little sassiness , don’t forget the power of the cone heel. It will get you through any dull day when skinny heels are out of the question. Edgy yet sophisticated, polished and pulled together, you’ll be teetering on the edge of good times.

Plus, they’re a guaranteed lower body workout; just 20 minutes per day and you’ll be well on your way to a maximum calorie burn.


// Copyright 2020 Google LLC
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

package aip0124

import (
	"testing"

	"github.com/googleapis/api-linter/rules/internal/testutils"
)

func TestReferenceSamePackage(t *testing.T) {
	for _, test := range []struct {
		name         string
		Field        string
		Ref          string
		OtherPackage string
		problems     testutils.Problems
	}{
		{"SamePkg", "type", "library.googleapis.com/Book", "same", nil},
		{"SamePkgChild", "child_type", "library.googleapis.com/Book", "same", nil},
		{"NotSamePkg", "type", "library.googleapis.com/Book", "other", testutils.Problems{{Message: "same package"}}},
		{"NotSamePkgChild", "child_type", "library.googleapis.com/Book", "other", testutils.Problems{{Message: "same package"}}},
		{"Ignored", "type", "cloudresourcemanager.googleapis.com/Project", "other", nil},
	} {
		t.Run(test.name, func(t *testing.T) {
			t.Run("DirectDependency", func(t *testing.T) {
				files := testutils.ParseProto3Tmpls(t, map[string]string{
					"dep.proto": `
						package {{.OtherPackage}};
						import "google/api/resource.proto";
						message Book {
							option (google.api.resource) = {
								type: "{{.Ref}}"
							};
						}
					`,
					"leaf.proto": `
						package same;
						import "google/api/resource.proto";
						import "dep.proto";
						message Foo {
							string book = 1 [(google.api.resource_reference).{{.Field}} = "{{.Ref}}"];
						}
					`,
				}, test)
				file := files["leaf.proto"]
				field := file.GetMessageTypes()[0].GetFields()[0]
				if diff := test.problems.SetDescriptor(field).Diff(referenceSamePackage.Lint(file)); diff != "" {
					t.Errorf(diff)
				}
			})

			t.Run("DirectDependencyResourceDefinition", func(t *testing.T) {
				files := testutils.ParseProto3Tmpls(t, map[string]string{
					"dep.proto": `
						package {{.OtherPackage}};
						import "google/api/resource.proto";
						option (google.api.resource_definition) = {
							type: "{{.Ref}}"
						};
					`,
					"leaf.proto": `
						package same;
						import "google/api/resource.proto";
						import "dep.proto";
						message Foo {
							string book = 1 [(google.api.resource_reference).{{.Field}} = "{{.Ref}}"];
						}
					`,
				}, test)
				file := files["leaf.proto"]
				field := file.GetMessageTypes()[0].GetFields()[0]
				if diff := test.problems.SetDescriptor(field).Diff(referenceSamePackage.Lint(file)); diff != "" {
					t.Errorf(diff)
				}
			})

			t.Run("RemoteDependency", func(t *testing.T) {
				files := testutils.ParseProto3Tmpls(t, map[string]string{
					"dep.proto": `
						package {{.OtherPackage}};
						import "google/api/resource.proto";
						message Book {
							option (google.api.resource) = {
								type: "library.googleapis.com/Book"
							};
						}
					`,
					"intermediate.proto": `import "dep.proto";`,
					"leaf.proto": `
						package same;
						import "google/api/resource.proto";
						import "intermediate.proto";
						message Foo {
							string book = 1 [(google.api.resource_reference).{{.Field}} = "{{.Ref}}"];
						}
					`,
				}, test)
				file := files["leaf.proto"]
				field := file.GetMessageTypes()[0].GetFields()[0]
				if diff := test.problems.SetDescriptor(field).Diff(referenceSamePackage.Lint(file)); diff != "" {
					t.Errorf(diff)
				}
			})
		})
	}
}


Q:

Solve(covMat) retorna que system is computationally singular: reciprocal condition number

Quiero obtener la cartera de variación mínima. Los rendimientos esperados mu son:
> mu
       .SXQR        .SXTR        .SXNR        .SXMR        .SXAR        .SX3R
 0.100496686  0.068652744  0.065081570  0.013155820  0.086947540  0.103143934
       .SX6R        .SXFR        .SXOR        .SXDR        .SX4R        .SXRR
 0.054990629  0.088484620  0.085435533  0.068080455  0.098365460  0.023932074
       .SXER        .SXKR        .SX7R        .SX8R        .SXIR        .SXPR
 0.037525561 -0.000400454  0.024776148  0.007051037  0.042215791  0.116013074

y la matriz de covarianza covMat esta :
> covMat
           .SXQR      .SXTR      .SXNR      .SXMR      .SXAR      .SX3R      .SX6R
.SXQR 0.03345763 0.03498086 0.04185753 0.03245136 0.03497776 0.02324828 0.02081399
.SXTR 0.03498086 0.04974472 0.04619830 0.04159817 0.04420657 0.02401824 0.02689768
.SXNR 0.04185753 0.04619830 0.06097311 0.04537355 0.05011720 0.02686316 0.03057380
.SXMR 0.03245136 0.04159817 0.04537355 0.04287405 0.04017447 0.02191462 0.02405812
.SXAR 0.03497776 0.04420657 0.05011720 0.04017447 0.05465295 0.02184147 0.02625680
.SX3R 0.02324828 0.02401824 0.02686316 0.02191462 0.02184147 0.02318865 0.01733667
.SX6R 0.02081399 0.02689768 0.03057380 0.02405812 0.02625680 0.01733667 0.03490965
.SXFR 0.04086303 0.05423479 0.05599539 0.04781758 0.04785298 0.03177379 0.03971822
.SXOR 0.03468033 0.04174388 0.04790487 0.03778244 0.03958789 0.02265676 0.03305845
.SXDR 0.01823918 0.02550628 0.02203189 0.02453928 0.01603731 0.01815483 0.01477641
.SX4R 0.03342966 0.03293408 0.04631396 0.03373207 0.03772380 0.02582638 0.02640921
.SXRR 0.03033003 0.03421856 0.04020604 0.03334523 0.03561357 0.01863272 0.02276777
.SXER 0.02051229 0.01525291 0.02833009 0.01743750 0.01769105 0.01464734 0.01775119
.SXKR 0.02694061 0.03196615 0.03950701 0.03682066 0.03574271 0.01394396 0.02498871
.SX7R 0.03635913 0.04453817 0.04871591 0.03789661 0.03882093 0.02804067 0.03282608
.SX8R 0.03991513 0.04959444 0.05847244 0.04934120 0.04838590 0.02522826 0.02852557
.SXIR 0.03508348 0.04831080 0.04905516 0.04555107 0.04046836 0.02949463 0.03263901
.SXPR 0.04456718 0.03223030 0.06505796 0.03031465 0.04557004 0.02648925 0.03399364
           .SXFR      .SXOR       .SXDR      .SX4R      .SXRR      .SXER      .SXKR
.SXQR 0.04086303 0.03468033 0.018239181 0.03342966 0.03033003 0.02051229 0.02694061
.SXTR 0.05423479 0.04174388 0.025506282 0.03293408 0.03421856 0.01525291 0.03196615
.SXNR 0.05599539 0.04790487 0.022031890 0.04631396 0.04020604 0.02833009 0.03950701
.SXMR 0.04781758 0.03778244 0.024539282 0.03373207 0.03334523 0.01743750 0.03682066
.SXAR 0.04785298 0.03958789 0.016037311 0.03772380 0.03561357 0.01769105 0.03574271
.SX3R 0.03177379 0.02265676 0.018154833 0.02582638 0.01863272 0.01464734 0.01394396
.SX6R 0.03971822 0.03305845 0.014776414 0.02640921 0.02276777 0.01775119 0.02498871
.SXFR 0.07060256 0.05433736 0.029870028 0.04370332 0.04173824 0.02543286 0.03772980
.SXOR 0.05433736 0.05018950 0.019754192 0.03724791 0.03814745 0.02642396 0.03293653
.SXDR 0.02987003 0.01975419 0.024627383 0.01758262 0.01499347 0.01045468 0.01481692
.SX4R 0.04370332 0.03724791 0.017582623 0.04093423 0.03116615 0.02429916 0.02793648
.SXRR 0.04173824 0.03814745 0.014993470 0.03116615 0.03504357 0.01910385 0.03251937
.SXER 0.02543286 0.02642396 0.010454676 0.02429916 0.01910385 0.02722964 0.01322536
.SXKR 0.03772980 0.03293653 0.014816920 0.02793648 0.03251937 0.01322536 0.04505911
.SX7R 0.05938230 0.05169770 0.023760635 0.04122183 0.03709132 0.02779035 0.02632013
.SX8R 0.05506206 0.04556889 0.027748962 0.04155255 0.03723654 0.02359730 0.04231239
.SXIR 0.05991709 0.04424346 0.033142798 0.03888777 0.03233359 0.02232765 0.03104647
.SXPR 0.04889303 0.05858437 0.006954027 0.05553596 0.04425855 0.05085459 0.02653357
           .SX7R      .SX8R      .SXIR       .SXPR
.SXQR 0.03635913 0.03991513 0.03508348 0.044567182
.SXTR 0.04453817 0.04959444 0.04831080 0.032230303
.SXNR 0.04871591 0.05847244 0.04905516 0.065057961
.SXMR 0.03789661 0.04934120 0.04555107 0.030314650
.SXAR 0.03882093 0.04838590 0.04046836 0.045570043
.SX3R 0.02804067 0.02522826 0.02949463 0.026489254
.SX6R 0.03282608 0.02852557 0.03263901 0.033993645
.SXFR 0.05938230 0.05506206 0.05991709 0.048893031
.SXOR 0.05169770 0.04556889 0.04424346 0.058584372
.SXDR 0.02376063 0.02774896 0.03314280 0.006954027
.SX4R 0.04122183 0.04155255 0.03888777 0.055535956
.SXRR 0.03709132 0.03723654 0.03233359 0.044258552
.SXER 0.02779035 0.02359730 0.02232765 0.050854589
.SXKR 0.02632013 0.04231239 0.03104647 0.026533566
.SX7R 0.06443470 0.04622553 0.04997693 0.062958984
.SX8R 0.04622553 0.06557348 0.05449832 0.047301440
.SXIR 0.04997693 0.05449832 0.06063113 0.032824422
.SXPR 0.06295898 0.04730144 0.03282442 0.143337184

He visto que hay este articulo que da la ecuación y el código:

Entonces utilizo el código siguiente.
assetSymbols <- colnames(yearly_return)

mu <- colMeans(yearly_return,na.rm = TRUE) # expected returns
covMat <- cov(yearly_return) # covariance matrix
corMat <- cor(yearly_return) # correlation matrix

## Minimum Variance Portfolio function ####
getMinVariancePortfolio <- function(mu,covMat,assetSymbols) {
  U <- rep(1, length(mu)) # vector of 1
  O <- solve(covMat)     # inverse of covariance matrix
  w <- O%*%U /as.numeric(t(U)%*%O%*% U)
  Risk <- sqrt(t(w) %*% covMat %*% w)
  ExpReturn <- t(w) %*% mu
  Weights <- `names<-`(round(w, 5), assetSymbols)
  list(Weights = t(Weights),
       ExpReturn = round(as.numeric(ExpReturn), 5),
       Risk = round(as.numeric(Risk), 5))
}

Pero calculando el inverso de la matriz obtengo:
 Error in solve.default(covMat) :
  system is computationally singular: reciprocal condition number = 1.06734e-19

A:

Consideraciones
Como la implementación de la función getMinVariancePortfolio proviene de aplicar el multiplicador de lagrange al siguiente enunciado de programación lineal producto del Modelo de Markowitz:

Luego de verificar su correcta resolución, aplicando las derivadas parciales respectivas:

Y siendo:

w: el peso de las acciones, Σ-1: matriz inversa de covarianza y u: un arreglo unitario cuya longitud es igual al número de acciones.

Sólo puedo decir que la matriz inversa de Σ no sólo tiene que ser "cuadrada" (que se cumple porque es una matriz de covarianza) sino que su determinante debe ser diferente de cero (0). Por ejemplo una matriz 2x2, Donde |A| es la determinante:

En este caso  (try(solve(covMat))) si se aplica det(covMat), debe ser un valor muy pequeño, casi muy cercano a cero (0).
Cómo se está usando multiplicadores de lagrange para resolver un sistema de ecuaciones, lo anterior implicaría que existen infinitas soluciones o dicho de otro modo, diferentes pesos (w) de rendimiento para las 18 acciones.
|covMat| = 0 : Infinitos pesos (w) luego de resolver las ecuaciones de lagrange

Lo cual tiene sentido porque 1/0 es infinito.
Para resolver lo anterior, se revisó la documentación de Wolfram Aplha sobre matrices inversas (inglés) ahí se explica que existen diversos métodos para su tratamiento.
En tal sentido, al revisar la documentación de la función solve en LAPACK — Linear Algebra PACKage, siento decir que no he sido capaz de encontrar con qué método dicha función determina la inversa de una matriz (cuadrada).

No obstante, como el procedimiento mostrado tanto en la pregunta como en el articulo (francés, sólo leí las ecuaciones :)) es correcto y la restricción sólo está en el método ha emplearse para determinar la inversa de una matriz NxN, sólo queda buscar otros métodos.

Sobre lo anterior, por lo general en algebra lineal se emplea la Pseudoinversa de Moore-Penrose para la resolución de ecuaciones lineales, que en este caso aplica, porque se ha usado los multiplicadores de lagrange a un problema de minimización de programación lineal.
Alternativa
A fin de no reinventar la rueda, el paquete pragma emplea la Pseudoinversa de Moore-Penrose para hallar matrices inversas.
Sólo hay que instalar dicho paquete y comprobar si efectivamente trabaja bien en contraste con la función solve
Tomándose el ejemplo que viene en solve sobre matriz de hilbert
install.packages(pracma)
library(pracma)

hilbert <- function(n) { i <- 1:n; 1 / outer(i - 1, i, "+") }
h8 <- hilbert(8); h8
          [,1]      [,2]      [,3]       [,4]       [,5]       [,6]       [,7]       [,8]
[1,] 1.0000000 0.5000000 0.3333333 0.25000000 0.20000000 0.16666667 0.14285714 0.12500000
[2,] 0.5000000 0.3333333 0.2500000 0.20000000 0.16666667 0.14285714 0.12500000 0.11111111
[3,] 0.3333333 0.2500000 0.2000000 0.16666667 0.14285714 0.12500000 0.11111111 0.10000000
[4,] 0.2500000 0.2000000 0.1666667 0.14285714 0.12500000 0.11111111 0.10000000 0.09090909
[5,] 0.2000000 0.1666667 0.1428571 0.12500000 0.11111111 0.10000000 0.09090909 0.08333333
[6,] 0.1666667 0.1428571 0.1250000 0.11111111 0.10000000 0.09090909 0.08333333 0.07692308
[7,] 0.1428571 0.1250000 0.1111111 0.10000000 0.09090909 0.08333333 0.07692308 0.07142857
[8,] 0.1250000 0.1111111 0.1000000 0.09090909 0.08333333 0.07692308 0.07142857 0.06666667

solve(h8) # funcion solve
        [,1]      [,2]       [,3]       [,4]        [,5]        [,6]        [,7]       [,8]
[1,]      64     -2016      20160     -92400      221760     -288288      192192     -51480
[2,]   -2016     84672    -952560    4656960   -11642400    15567552   -10594584    2882880
[3,]   20160   -952560   11430720  -58212000   149688000  -204324119   141261119  -38918880
[4,]  -92400   4656960  -58212000  304919999  -800414996  1109908794  -776936155  216215998
[5,]  221760 -11642400  149688000 -800414996  2134439987 -2996753738  2118916783 -594593995
[6,] -288288  15567552 -204324119 1109908793 -2996753738  4249941661 -3030050996  856215352
[7,]  192192 -10594584  141261119 -776936154  2118916782 -3030050996  2175421226 -618377753
[8,]  -51480   2882880  -38918880  216215998  -594593995   856215351  -618377753  176679358

pinv(h8) # función del paquete Pragma
        [,1]      [,2]       [,3]       [,4]        [,5]        [,6]        [,7]       [,8]
[1,]      64     -2016      20160     -92400      221760     -288288      192192     -51480
[2,]   -2016     84672    -952560    4656960   -11642400    15567552   -10594584    2882880
[3,]   20160   -952560   11430720  -58211999   149687996  -204324114   141261116  -38918879
[4,]  -92400   4656960  -58211999  304919992  -800414977  1109908766  -776936135  216215993
[5,]  221760 -11642400  149687996 -800414977  2134439936 -2996753666  2118916732 -594593980
[6,] -288288  15567552 -204324114 1109908767 -2996753668  4249941561 -3030050925  856215332
[7,]  192192 -10594584  141261116 -776936136  2118916733 -3030050926  2175421177 -618377739
[8,]  -51480   2882880  -38918879  216215993  -594593981   856215332  -618377740  176679354

Cómo son métodos diferentes de aproximación, los resultados presentarán pequeñas variaciones, pero esto no invalida su uso para este caso concreto.
Solución
Una vez instalado y llamado el paquete pragma
install.packages(pracma)
library(pracma)

Sólo hay que reemplazar solve por pinv en la función getMinVariancePortfolio
## Minimum Variance Portfolio function ####
getMinVariancePortfolio <- function(mu,covMat,assetSymbols) {
    U <- rep(1, length(mu) # vector of 1
    O <- pinv(covMat)      # inverse of covariance matrix: Pragma Function pinv
    w <- O%*%U /as.numeric(t(U)%*%O%*% U)
    Risk <- sqrt(t(w) %*% covMat %*% w)
    ExpReturn <- t(w) %*% mu
    Weights <- `names<-`(round(w, 5), assetSymbols)
    list(Weights = t(Weights),
         ExpReturn = round(as.numeric(ExpReturn), 5),
         Risk = round(as.numeric(Risk), 5))
}

Al probar lo anterior con la estructura de datos facilitada en Calcular la matriz de covarianza se obtiene lo siguiente:
assetSymbols <- colnames(yearly_return)
mu <- colMeans(yearly_return,na.rm = TRUE) # expected returns
covMat <- cov(yearly_return) # covariance matrix

getMinVariancePortfolio(mu,covMat,assetSymbols)

$Weights
         [,1]    [,2]     [,3]    [,4]    [,5]    [,6]    [,7]    [,8]    [,9]   [,10]   [,11]   [,12]
[1,] -0.12839 0.01941 -0.27081 0.09285 0.13149 0.12208 0.24466 0.16166 0.25637 0.06266 0.01619 0.34199
       [,13]    [,14]   [,15]    [,16]  [,17]   [,18]
[1,] 0.13703 -0.05763 0.00859 -0.37557 0.0433 0.19411

$ExpReturn
[1] 0.12518

$Risk

[1] 0.15789

Finalmente, vale la pena acotar que la determinante para la matriz de covarianza (covMat) aún siendo muy pequeña:
det(covMat)
[1] -3.634388e-231

No impidió que se le encontrara su inversa con el método de la Pseudoinversa de Moore-Penrose.

Nota: Sólo aclarar qué no toda matriz cuadra tiene inversa:
   det(matrix(1:9,nrow=3))== 0 # TRUE
   por eso se hizo necesario emplear la matriz de hilbert para comprobar las inversas entre solve y pinv.

Ampliación respuesta
En wikipedia Moore–Penrose inverse - Inglés en la sección Software libraries se menciona que paquetes emplean esta técnica:

NumPy y SciPy de Python
LAPACK (aunque este tiene un desarrollo diferente del SVD-Singular value decomposition)
Octave también lo emplea a través de una función pinv
Y por supuesto R a través del paquete pragma::pinv y MASS::ginv este último lo he probado y también arroja los resultado expuestos.

Sólo hacer lo siguiente:
install.packages(MASS)
library(MASS)

# ----------------------------------------------------------------------
# dentro de la funcion "getMinVariancePortfolio"
# ----------------------------------------------------------------------
 O <- ginv(covMat)     # inverse of covariance matrix: Funcion de Mass
# ----------------------------------------------------------------------

# Se llama la función
getMinVariancePortfolio(mu,covMat,assetSymbols)

$Weights
         [,1]    [,2]     [,3]    [,4]    [,5]    [,6]    [,7]    [,8]    [,9]   [,10]   [,11]   [,12]
[1,] -0.12839 0.01941 -0.27081 0.09285 0.13149 0.12208 0.24466 0.16166 0.25637 0.06266 0.01619 0.34199
       [,13]    [,14]   [,15]    [,16]  [,17]   [,18]
[1,] 0.13703 -0.05763 0.00859 -0.37557 0.0433 0.19411

$ExpReturn
[1] 0.12518

$Risk
[1] 0.15789


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Hydro and Cache Women Win Miss SWOSU Titles

Submitted by Edgar on Wed, 11/13/2013 - 2:34pm

Hailey Raetz, a Hydro junior at Southwestern Oklahoma State University, won the crown of Miss SWOSU 2014, while 17-year-old student Even Mazur of Cache High School won the title of Miss SWOSU’s Outstanding Teen at Saturday’s (November 9) pageants.


The
seeds of this creative outlet we call Sawblade Software were
sewn a long while ago. During our formative years we drew a lot
of pictures, played a lot of Super Nintendo, learned how to blow
stuff up, discovered some really cool music, and filmed some sick movies.
There was an attempt to make a huge game based on the Marathon engine, but the project was
too ambitious and the level design tools were too buggy.
Then things really started going downhill: growing up meant
sitting in traffic jams on commuter highways, paying taxes,
and struggling to survive a day at the office after the requisite
catharsis of a Cradle of Filth concert. So I bailed. This
Sawblade Software thing is no opiate, but it's a temporary
and, God willing, profitable escape to a place where the
work is meaningful, the hours are flexible, and the people
all around are much more alive.

Fabricating Fun, Flushing Frustration
We all seem to have more fun when we're making things. Drawing,
building, composing, programming, writing, sculpting... there
are a lot of outlets for creativity. And here, at least in
theory, is another one: Power Game Factory. We're guessing
that video games could be even more fun to make than they are
to play, at least if it weren't for the challenges accompanying computer
programming. That's why Power Game Factory was designed to let you avoid
those technical roadblocks and focus on the creative aspects of game
design. We think that anyone who puts some effort into using Power Game
Factory could end up with a cool project and a potentially large, appreciative
audience.

Welcome,
Mac Addicts
Sawblade Software designs software for the Macintosh because it's a
great computer... and because we have no clue how to make this stuff
work on Windows. We admire the Bungie Software of the 90s: a creative
force that understood what the Mac was all about and gave people what
they wanted, with a few surprises thrown in. While we can't match Bungie's
volume of output, we can certainly work in their spirit while striving
to make the most of our limited potential.

Read on to become an expert on Sawblade
Software's murky past and peculiar present. Watch out for all the half-truths;
take everything with a grain of salt (except for the bit about our contributions
to the World Food Programme.)

October 2000Sawblade Software's founder figures out how to program in Java
class. The fruits of his labor survive to this day, but they'recrap.

September 27, 2001The first lines of code are written for Greenland Invasion, a
side-scroller for the Mac, designed as a college thesis project.

April 26, 2002Greenland Invasion makes its debut
in a packed auditorium at Hampshire College. Four volunteers
are picked from the audience to compete for the highest
score. The contest ensues flawlessly, followed by much
hugging and hand-shaking.

July 8, 2002The first copy of The Green Machine is sold for $15. It is an
enhanced version of Greenland Invasion with completely modifiable
game content.

August 4, 2002Work begins on a user friendly side scrolling game design application
called Power Game Factory. It would eventually emerge as
a huge improvement over The Green Machine.

March 30, 2004Sawblade Software's founder quits his
day job due to his intent to experience a life of bliss.
Even with all the free time in the world, he somehow still
can't manage to finish Power Game Factory.

October 1, 2004After two years of relatively hard work on Power Game Factory,
it is feature complete and largely free of bugs.

January 2005The Power Game Factory box and promotional
materials are designed and sent to press.

Later in 2005Power Game Factory is released. The Macintosh community braces
for a slew of bad 2D games.

2007-2008Numerous Power Game Factory 1.1 beta releases
are showered upon unsuspecting forum readers.

Programming Language used: Power Game Factory was originally programmed in REALbasic
4.5.2. It has 126991 lines of code, not including comments. The
game engine used REALbasic 5.5.5. The newest version of the engine
uses REALbasic 2008 Release 5, and
utilizes tools provided by Monkeybread Software and the
TinRocket SuperSpriteSurface framework.

Official Programming Music: Disco
Volante, by Mr. Bungle [we found the secret song!]

Official Driving to the Post Office Music: Mit
Gas, by Tomahawk, released 2003 [it's very ominous.]

Favorite Mac Game That Was Never Released: Project Skatepark [an
ingenious hybrid of Castlevania, Tony Hawk's Pro Skater, and the
archetypical Japanese Dating Simulation, set in a modern-day New
Jersey apartment complex that looks like it belongs in the Weimar
Republic of the late 1920s. One of the project leaders is now employed
by Oracle.]

Exit Strategy: The
dissolution of the company, and the even division of assets
and fat wads of cash among everyone involved.

We Work In A Boat!
Sawblade Software makes its home in a toxic cargo vessel that we salvaged
from the
Alang shipbreaking yard. When we first discovered the ship,
it was full of asbestos, lead paint, PCBs and explosive gases. We didn't
want the workers at Alang (see photo)
to be exposed to the ship's dangers, so we smuggled it to a secret location near
the coast of the Fairly
Fruited Plain
and set to work restoring
it and converting its lower decks into office space.

As you can
see, our facilities still aren't
sterile, but Julie promises to disinfect everything when she returns
from her latest mooseriding expedition. We like it here. See the
smokestack? Julie's cat Uji jumped off it and fell right through the
roof of the cabin. He's ok though.

Amidst the Stench, a Social Conscience
Our experience at the Alang shipbreaking yard reminded us that all
is not well with the world. Poverty, sub-par working conditions, and
inequality threaten to halt the progress of the developing world, and
we want to do our part to promote change. That's why five percent of
Sawblade Software's earnings are donated to the United Nations World
Food Programme, one of the most important organizations in the fight
against global hunger.

Corporate Info
Sawblade Software is a sole proprietorship based in Litchfield, Connecticut.
As explained in our privacy
statement, we will not share your personal
information with anyone. Our software comes with a license
agreement that you'll find to be more relaxed than usual. We think that
by letting you make a copy of your Power Game Factory CD for a friend,
we'll earn karma points and the people at Slashdot won't hate us so much. Read
the license here.


Synergistic anion-directed coordination of ferric and cupric ions to bovine serum transferrin--an inorganic perspective.
A series of new iron(III) and copper(II) complexes of bovine serum transferrin (BTf), with carbonate and/or oxalate as the synergistic anion, are presented. The complexes [Fe(2)(CO(3))(2)BTf], [Fe(2)(C(2)O(4))(2)BTf], [Cu(2)(CO(3))(2)BTf] and [Cu(C(2)O(4))BTf] were prepared by standard titrimetric techniques. The oxalate derivatives were also obtained from the corresponding carbonate complexes by anion-displacement. The site-preference of the transition metal-oxalate synergism has facilitated the preparation and isolation of the mononuclear complex [Cu(C(2)O(4))BTf], the mixed-anion complexes [Cu(2)(CO(3))(C(2)O(4))BTf] and [Fe(2)(CO(3))(C(2)O(4))BTf] and the mixed-metal complex [FeCu(C(2)O(4))(2)BTf]. The sensitivity of electron paramagnetic resonance (EPR) spectroscopy to the nature of the synergistic anions at the specific-binding sites of the transferrins has made this physical technique particularly indispensable to this study. None of the other members of the transferrin family of proteins has ever been demonstrated to bind the ferric and cupric ions one after the other, each occupying a separate specific-binding site of the same transferrin molecule, as a response to the coordination restrictions imposed by the oxalate ion. The bathochromic shift of the visible p(pi)-d(pi*) CT band for iron(III)-BTf and the hypsochromic shift of the p(pi)-d(sigma*) CT band for copper(II)-BTf, on replacing carbonate by oxalate as the associated anion, are consistent with the relative positions of these anionic ligands in the spectrochemical series and the nature of the d-type acceptor orbitals involved in the CT transitions. The binding and spectroscopic properties of bovine serum transferrin--a serum transferrin--very nearly mirror those of human serum transferrin, but differ significantly from those of human lactoferrin.


#ifndef ANT_CHANNEL_CONFIG_H__
#define ANT_CHANNEL_CONFIG_H__

/** @file
 *
 * @defgroup ant_sdk_channel_config ANT channel configuration
 * @{
 * @ingroup ant_sdk_utils
 * @brief ANT channel configuration module.
 */

#include <stdint.h>
#include "ant_stack_config_defs.h"

#ifndef ANT_CONFIG_ENCRYPTED_CHANNELS
    #error Undefined ANT_CONFIG_ENCRYPTED_CHANNELS. It should be defined in ant_stack_config_defs.h file.
#elif ANT_CONFIG_ENCRYPTED_CHANNELS > 0
    #include "ant_encrypt_config.h"
#endif

/**@brief ANT channel configuration structure. */
typedef struct
{
    uint8_t  channel_number;        ///< Assigned channel number.
    uint8_t  channel_type;          ///< Channel type (see Assign Channel Parameters in ant_parameters.h: @ref ant_parameters).
    uint8_t  ext_assign;            ///< Extended assign (see Ext. Assign Channel Parameters in ant_parameters.h: @ref ant_parameters).
    uint8_t  rf_freq;               ///< Radio frequency offset from 2400 MHz (for example, 2466 MHz, rf_freq = 66).
    uint8_t  transmission_type;     ///< Transmission type.
    uint8_t  device_type;           ///< Device type.
    uint16_t device_number;         ///< Device number.
    uint16_t channel_period;        ///< The period in 32 kHz counts.
    uint8_t  network_number;        ///< Network number denoting the network key.

#if ANT_CONFIG_ENCRYPTED_CHANNELS > 0
    ant_encrypt_channel_settings_t * p_crypto_settings; ///< Pointer to cryptographic settings, NULL if this configuration have to be omitted.
#endif

} ant_channel_config_t;

/**@brief Function for configuring the ANT channel.
 *
 * @param[in]  p_config        Pointer to the channel configuration structure.
 *
 * @retval     NRF_SUCCESS     If the channel was successfully configured. Otherwise, an error code is returned.
 */
uint32_t ant_channel_init(ant_channel_config_t const * p_config);

#endif // ANT_CHANNEL_CONFIG_H__
/** @} */


Physical Therapy Management of Patients With Chronic Low Back Pain and Hip Abductor Weakness.
Hip abductor dysfunction is common in individuals with chronic low back pain (CLBP). Previous research investigating abductor strengthening in the heterogeneous CLBP population is sparse and has failed to target those patients most likely to benefit. The aim of the current case series was to describe the physical therapy management and outcomes of 3 patients with CLBP matching a previously identified subgroup characterized by substantial hip abductor weakness. Three nonconsecutive patients with CLBP-a 77-year-old man, a 78-year-old woman, and an 85-year-old woman-were treated in an outpatient physical therapy clinic. All 3 patients matched a previously identified CLBP subgroup characterized by substantial hip abductor weakness. Patients were treated using a targeted exercise approach consisting mostly of hip abductor strengthening for 11 to 17 visits over 8 to 10 weeks. Patients received additional treatments including heel lift and pain neuroscience education when indicated. By discharge, all patients had made clinically important improvements in pain (3- to 7-point reduction on the Numeric Pain Rating Scale), function (10- to 16-point change on the Modified Oswestry Disability Index), and perceived improvement (6-7 on Global Rating of Change Scale). Lumbar range of motion was painless, and hip abductor strength was improved from 2+/5 to 3+/5 in all 3 patients. These gains were maintained at 3-month follow-up. The current case series describes the use of a targeted exercise approach consisting mostly of hip abductor strengthening in a group of patients with CLBP and hip abductor weakness. The results indicated that this approach may be effective in reducing pain and improving function, particularly for older patients.


[Thoracic myelography with water-soluble contrast medium (metrizamide) (author's transl)].
The use of water-soluble contrast media for the thoracic myelography has become possible with the introduction of Metrizamide (Amipaque). A modification of the technique used with oily contrast media results in excellent demonstration of detail of intraspinal structures and of pathological changes. The medium is well tolerated and does not cause irritation of the spinal cord; the results must be regarded as excellent.


<?xml version="1.0" encoding="UTF-8"?>
 <!DOCTYPE html PUBLIC  "-//CL//DTD XHTML 1.0 Transitional plus Embed//EN"
 "http://www.w3.org/Graphics/xhtml1-transitional-plus-embed.dtd">

 <meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
 <meta name="keywords" content="W3C SVG 1.1 Test Suite testsuite mobile"/>
 <meta name="description" content="W3C SVG 1.2 Tiny Test Suite"/>
 <title>
SVG 1.2 Tiny test:paint-color-04-t </title>

Tiny version

Specification link: 11.13 Color

    paint-color-03-t ←
    index
    → paint-color-05-t

paint-color-04-t

							SVG Image

							PNG Image

   	    		  			<embed src="../svggen/paint-color-04-t.svg" width="480" height="360"/>

        Tests system colors. The colors on your screen might not match the reference image at all, but they should at
        minimum be legible and should preferably resemble the colors used on menus and other user interface elements on
        your computer, pda or phone.

				paint-color-03-t ←
				index
				→ paint-color-05-t


Enhancement of substrate-gated Cl- currents via rat glutamate transporter EAAT4 by PMA.
Glutamate transporters (also called excitatory amino acid transporters, EAAT) are important in extracellular homeostasis of glutamate, a major excitatory neurotransmitter. EAAT4, a neuronally expressed EAAT in cerebellum, has a large portion (approximately 95% of the total L-aspartate-induced currents in human EAAT4) of substrate-gated Cl(-) currents, a distinct feature of this EAAT. We cloned EAAT4 from rat cerebellum. This molecule was predicted to have eight putative transmembrane domains. L-glutamate induced an inward current in oocytes expressing this EAAT4 at a holding potential -60 mV. Phorbol 12-myristate 13-acetate (PMA), a protein kinase C (PKC) activator, significantly increased the magnitude of L-glutamate-induced currents but did not affect the apparent affinity of EAAT4 for L-glutamate. This PMA-enhanced current had a reversal potential -17 mV at extracellular Cl(-) concentration ([Cl(-)](o)) 104 mM with an approximately 60-mV shift per 10-fold change in [Cl(-)](o), properties consistent with Cl(-)-selective conductance. However, PMA did not change EAAT4 transport activity as measured by [(3)H]-L-glutamate. Thus PMA-enhanced Cl(-) currents via EAAT4 were not thermodynamically coupled to substrate transport. These PMA-enhanced Cl(-) currents were partially blocked by staurosporine, chelerythrine, and calphostin C, the three PKC inhibitors. Ro-31-8425, a PKC inhibitor that inhibits conventional PKC isozymes at low concentrations (nM level), partially inhibited the PMA-enhanced Cl(-) currents only at a high concentration (1 microM). Intracellular injection of BAPTA, a Ca(2+)-chelating agent, did not affect the PMA-enhanced Cl(-) currents. 4alpha-Phorbol-12,13-didecanoate, an inactive analog of PMA, did not enhance glutamate-induced currents. These data suggest that PKC, possibly isozymes other than conventional ones, modulates the substrate-gated Cl(-) currents via rat EAAT4. Our results also suggest that substrate-gated ion channel activity and glutamate transport activity, two EAAT4 properties that could modulate neuronal excitability, can be regulated independently.


Multicoloured Jersey Boxer 3 Pack - M

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Update your underwear essentials with this pure cotton 3 pack of boxers. Crafted in a loose fit, they feature a wide soft brushed elasticated waistband, a functional button fly and an antibacterial finish to keep you fresh. They also have a printed care label to prevent irritation.

1 x Green

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1 x Burgundy

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Model wears a size M

Model's height is 6' 2"

The small print

*Prices correct as displayed but are subject to change.

The customer and brand answers you’ll see above are submitted independently. As we don’t review these answers, we can’t take responsibility for anything they may say. The responses from Argos colleagues are accurate at the time of publishing. For the latest info, you should check the product page.


Decision Tree for NodeJS
========================

This module contains the NodeJS Implementation of Decision Tree using [ID3 Algorithm](http://en.wikipedia.org/wiki/ID3_algorithm)

# Table Of Contents
* [`Installation`](#installation)
* [`Usage`](#usage)
	* [`Import Module`](#installation)
	* [`Prepare`](#installation)
	* [`Installation`](#installation)

# [Installation](id:installation)
	npm install decision-tree

# [Usage](id:usage)

* Import the module:

		var DecisionTree = require('decision-tree');

* Prepare training dataset:

		var training_data = [
			{"color":"blue", "shape":"square", "liked":false},
			{"color":"red", "shape":"square", "liked":false},
			{"color":"blue", "shape":"circle", "liked":true},
			{"color":"red", "shape":"circle", "liked":true},
			{"color":"blue", "shape":"hexagon", "liked":false},
			{"color":"red", "shape":"hexagon", "liked":false},
			{"color":"yellow", "shape":"hexagon", "liked":true},
			{"color":"yellow", "shape":"circle", "liked":true}
		];

* Prepare test dataset:

		var test_data = [
			{"color":"blue", "shape":"hexagon", "liked":false},
			{"color":"red", "shape":"hexagon", "liked":false},
			{"color":"yellow", "shape":"hexagon", "liked":true},
			{"color":"yellow", "shape":"circle", "liked":true}
		];

* Setup Target Class used for prediction:

		var class_name = "liked";

* Setup Features to be used by decision tree:

		var features = ["color", "shape"];

* Create decision tree and train model:

		var dt = new DecisionTree(training_data, class_name, features);

* Predict class label for an instance:

		var predicted_class = dt.predict({
			color: "blue",
			shape: "hexagon"
		});

* Evaluate model on a dataset:

		var accuracy = dt.evaluate(test_data);

* Export underlying model for visualization or inspection:

		var treeJson = dt.toJSON();

* Alternately, create a decision tree from a previously trained model:

		var treeJson = dt.toJSON();
		var preTrainedDecisionTree = new DecisionTree(treeJson);


Q:

F# XML Data parsing a ''subtype''

So I'm using the FSharp.Data library and I have a generated type as such:
<ArrayOfCar>
  <Car>
    <LicenseNumber>000</LicenseNumber>
    <ProductionYear>2014</ProductionYear>
    <Type>Audi</Type>
  </Car>
  <Car>
    <LicenseNumber>999</LicenseNumber>
    <ProductionYear>2012</ProductionYear>
    <Type>BMW</Type>
  </Car>
</ArrayOfCar>

Now I have a question, as it seems the F# compiler will generate two types from this, ArrayOfCars and Car.
Now I'm calling an API that will return either the example above for a collection of cars and also a single Car with Car then being the root element. However I can only parse ArrayOfCars using ArrayOfCars.Parse there is no Car.Parse as far as I can see.
Is there something I'm missing here or must I then generate a seperate type for Car to handle when it is the root element?

A:

This is a very good question! This does not quite work in the current version of F# Data, but I consider that a bug, so I submitted a pull request which fixes this. The solution below uses the fixed version of F# Data, so you might need to build it from source.
You can pass multiple samples to the XML provider using the IsSampleList=true parameter. Then you can specify that all elements with the same name should be inferred as the same type using Global=true:
type C = XmlProvider<"""
  <Samples>
    <ArrayOfCar>
      <Car><Type>Audi</Type></Car>
      <Car><Type>BMW</Type></Car>
    </ArrayOfCar>
    <Car><Type>Trabant</Type></Car>
  </Samples>""", SampleIsList=true, Global=true>

With these parameters (and the fix), F# Data now treats Car as the same type in both of these samples, so all you have to do is to read either the Car node with a single car or ArrayOfCar with multiple cars:
let readCars str =
  let doc = C.Parse(str)
  match doc.Car, doc.ArrayOfCar with
  | Some car, _ -> [| car |]
  | _, Some cars -> cars.Cars

This function can now read both formats:
readCars "<Car><Type>Audi</Type></Car>"
|> Seq.iter (fun c -> printfn "%s" c.Type)
readCars "<ArrayOfCar><Car><Type>Audi</Type></Car><Car><Type>BMW</Type></Car></ArrayOfCar>"
|> Seq.iter (fun c -> printfn "%s" c.Type)


// Copyright (C) 2015 The Android Open Source Project
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

package com.google.gerrit.server.git;

import static com.google.common.base.Preconditions.checkState;

import com.google.gerrit.entities.Project;
import com.google.gerrit.lifecycle.LifecycleModule;
import com.google.gerrit.server.config.GerritServerConfig;
import com.google.gerrit.server.config.RepositoryConfig;
import com.google.gerrit.server.config.SitePaths;
import com.google.inject.Inject;
import com.google.inject.Singleton;
import java.nio.file.Path;
import org.eclipse.jgit.lib.Config;

/**
 * RepositoryManager that looks up repos stored across directories.
 *
 * <p>Each repository has a path configured in Gerrit server config, repository.NAME.basePath,
 * indicating where the repo can be found
 */
@Singleton
public class MultiBaseLocalDiskRepositoryManager extends LocalDiskRepositoryManager {

  public static class Module extends LifecycleModule {
    @Override
    protected void configure() {
      bind(GitRepositoryManager.class).to(MultiBaseLocalDiskRepositoryManager.class);
      listener().to(MultiBaseLocalDiskRepositoryManager.Lifecycle.class);
    }
  }

  private final RepositoryConfig config;

  @Inject
  MultiBaseLocalDiskRepositoryManager(
      SitePaths site, @GerritServerConfig Config cfg, RepositoryConfig config) {
    super(site, cfg);
    this.config = config;

    for (Path alternateBasePath : config.getAllBasePaths()) {
      checkState(
          alternateBasePath.isAbsolute(),
          "repository.<name>.basePath must be absolute: %s",
          alternateBasePath);
    }
  }

  @Override
  public Path getBasePath(Project.NameKey name) {
    Path alternateBasePath = config.getBasePath(name);
    return alternateBasePath != null ? alternateBasePath : super.getBasePath(name);
  }

  @Override
  protected void scanProjects(ProjectVisitor visitor) {
    super.scanProjects(visitor);
    for (Path path : config.getAllBasePaths()) {
      visitor.setStartFolder(path);
      super.scanProjects(visitor);
    }
  }
}


The Co-principal Investigators of The Study are Robert F. Anda, MD, MS, with the CDC; and Vincent J. Felitti, MD, with Kaiser Permanente.

Over 17,000 Kaiser patients participating in routine health screening volunteered to participate in The Study. Data resulting from their participation continues to be analyzed; it reveals staggering proof of the health, social, and economic risks that result from childhood trauma.

As a neuroscience student, I was particularly interested to catch up on Charlie Rose's year-long "Brain" series, which featured top experts in the field. For those of you who haven't watched it, here is my "cheat sheet" on the first episode.

Topic Overview

Making sense of our experiences with the world around us is a problem philosophers have wrestled with for centuries. Modern neuroscientists think that, with the recent advances in science, they are poised to solve it.

The brain is the great frontier in the pursuit of understanding everyone's favorite subject, ourselves. The brain is at the center of our individuality. Throughout history, we've attempted to shine light on the human experience through literature, art and philosophy as well as biology. Neuroscience is a natural bridge between the humanities and biological science. Scientific advances have helped us understand how the brain processes consciousness, free will, perception, cognition, emotion and memory.

Featured ResearchersTo delve into the intricacies of the brain, Rose turned to the experts—leading neuroscientists and philosophers. Nobel-laureate and pioneering memory neuroscientist Eric Kandel joined Rose as the co-host of this round table discussion. Participants included John Searle, preeminent philosopher of free will in the brain; Gerald Fischbach, neurologist and autism expert; Cornelia Bargmann, who studies the brains of microscopic worms; and Anthony Movshon, a psychologist and neuroscientist who studies the visual system of monkeys. Together, they discussed our current understanding of the brain, its structure, and the keys to cracking the mysteries that still confront us.

Key Insights

The human mind is created from the activity of our brain cells; without these cells we couldn't see, think or decide what to have for dinner.

We are one part nature, one part nurture.There is a genetically-determined, universal logic behind the brain's macro-architecture. All human brains are put together similarly, with two hemispheres and the same regional specificity for seeing, hearing and feeling. On a smaller level, every brain is unique based upon the person's experiences and the things they've learned. Each human brain has a hippocampus that looks roughly the same and serves the same function, but the memoriescontained within the hippocampus are as unique as our fingerprints.

The brain is constantly changing.The brain is not hard-wired, as was once believed. Everything we do in the course of our lives, from reading a book to chatting with our friends, causes our brains to change. As we learn, the brain must adapt to store that knowledge. The brain creates memories by strengthening or establishing new connections between cells. Conversely, by breaking the connections between cells, memories can be forgotten. This can happen on a short-term basis, like we when hear a telephone number, but then can't recall it ten minutes later. In this case, the brain undergoes a functional change, but it doesn't undergo an anatomical change. When we learn something on a long-term basis, part of the brain's anatomy is forever different. Cells restructure to account for the memory, and actively maintain the new structure for as long as the memory persists.

The complexity of the brain lies in the cell, the most basic unit of life. It is not the size of our brain or the number of cells we possess that provides us with extraordinary processing power. Human intelligence arises from the genetic code that tells our brain cells how to function. This code is responsible for creating the connections between cells, the unique structure of our brains and our ability to adapt to our environment.

Our brain is amazingly fragile.The brain, a three pound organ, consumes 20% of all the body's energy. A lapse in blood flow for a few seconds will cause the death of thousands of cells, as they're deprived of the vital energy from blood. A muscle cell, by contrast, can be deprived of blood for minutes at a time without serious damage.

Brain malfunction is instructive.One of the best ways to understand the brain is to observe it when it's not working. When a brain region is damaged, through a stroke, injury or disease, we gain insight into the purpose of that region. One of the first examples comes from the work of Paul Broca, a French physician and anatomist during the mid-19th century. Broca had a patient who had lost the ability to speak, but otherwise had no change in mental function. When this patient died, Broca did an autopsy and found a syphilitic lesion in the frontal part of the left hemisphere of his brain. "We speak with the left hemisphere," Broca announced. This gave us concrete evidence that the brain's functions were localized to specific regions and demonstrated the area responsible for language, now known as Broca's Region.

Analysis and Future Directions

Unsolved mysteries of the brain.Understanding how the brain turns our sensory experiences into a conscious reality is a three-step process. First we must find the neural correlates of activity. What brain regions, and which cells, are active during experiences and actions? Second we must determine whether this relationship is causal, or merely a correlation. Is that particular brain region necessary for an action or experience to take place? Finally, this must be synthesized into a theory. We need a framework to place the idea in to see if it can explain complex phenomena.

The elegance of modern neuroscience is the ability to study simple systems and apply the findings to complex systems. The principles of brain function hold true across species; we have a genetically-determined structure and cells learn through strengthening or creating connections. Much of our insight into human learning comes from research on the genetic and cellular properties of worm and slug brains.

The brain is the executive officer of our personhood, and it oversees the productivity of all the branches which comprise our conscious experience, from vision to language. Although there are discrete compartments of the brain responsible for each of our individual senses and abilities, we don't experience a segmented reality. We experience one cohesive reality that is qualitative and subjective. This gets into consciousness, creativity and free will. But how does the brain do it? As Kandel concludes, "This is the most profound question western thought has ever asked, and we're beginning to mass the troops to answer it."

I've been catching up on Charlie Rose's brain series. The second episode is all about the tricky and fascinating world of perception.

Brief Topic Overview

Trying to determine which of our senses is most important is like asking which leg best helps us walk: I'm thankful for each of them and would rather not give up any. Something fairly more certain is that asking this question can inspire a spirited discussion.

In terms of neuroscience, a good argument can be made for the value of sight. Roughly a quarter of our brain is devoted to vision, and this hefty portion is among the best understood. A long line of neuroscience careers have achieved fame because of their discoveries in the visual system. The advances in our grasp of the visual system have informed our view of the entire brain; it is a model for how other systems function. By understanding how the brain processes vision, we can make inferences about how the brain works as a whole.

I've often felt that visual systems neuroscientists think of themselves as an elite crowd of brain scholars, studying more important questions than the average stock. I imagine them confiding in each other, "You know, if God were a neuroscientist, He would study the visual system."

Featured ResearchersTo tackle this topic, Charlie Rose and co-host Eric Kandel were joined by top scholars of the brain's visual system. Occupying seats at the round table were Anthony Movshon, who studies the visual cortex of monkeys; Ted Adelson, a researcher trying to create machines that can see; Nancy Kanwisher, a leader in the study of human facial perception; and Pawan Sinha, who studies brain development and is renowned for restoring sight to children born blind due to cataracts. With their combined expertise, they discussed how the brain processes the visual world, from faces and landscapes to optical illusions.

Key Insight from the Program

The eye is not a cameraWhen you snap a shot of your buddies with your digital camera, the image is captured, pixel by pixel, exactly as it appears in front of you. The camera accurately reports what colors it sees, where it sees them and how bright they are. That's not how we see the world. Gestalt psychology shows that we see images as whole objects, not simply a series of lines and colors. We draw out contrasts, such as edges and shadows, to help reconstruct a three-dimensional world in our brains. You can recognize a tree at dawn, noon and dusk even though the colors look different in these three light conditions. Processing images as objects helps explain why humans are far better at recognizing faces than computers.

According to Movshon, "Humans can throw away useless information, whereas a computer can't. We can't see a flat cube. Even if it's drawn on paper, it appears three-dimensional. "

Visual computations are hierarchicalThe visual system works like an assembly line. When light enters the eye, it comes as raw, unprocessed material, but at the other end it comes out as a finished product. The eye's photoreceptor cells respond to dots of light and begin organizing these dots before sending them off to the brain. In the primary visual cortex, the brain receives the dots and puts them together into contiguous lines and streams of color. These lines and colors move on to more sophisticated visual regions, where they're packaged as an object, such as a face. From there, it can be compared to faces in your memory, and if it matches your grandma, you know to say hello and give her a hug. If it's not her, you won't be surprised if you get slapped after calling her Grandma.

Much of our understanding of the visual system came from the pivotal findings that earned Hubel and Wiesel the Nobel Prize. They showed awake cats images on a screen while recording from different brain regions. Early regions in the visual stream responded any time the cat was shown a light. However, while recording from the visual cortex, they found that cells responded only to lines in specific orientations. Some cells liked horizontal lines, while others responded to vertical lines. An individual cell in the brain is not like a pixel in a digital image. Your brain doesn't see an image that resembles a photograph, but it breaks down images into their components, an amalgam of lines and curves arranged in a variety of orientations. Edges combine to create corners, and from this we get shapes that eventually become faces.

Functions are localizedEach area of the brain carries out a specific function that's crucial to our visual experience. There's a part of our brain called the fusiform gyrus that only turns on when we look at a face. If the fusiform gyrus is damaged, you can no longer recognize your mother by sight. There's also a region that recognizes landscapes called the parahippocampal place area. In one case, a man who had damage to the parahippocampal place area on both sides of his brain was able to get around and recognize faces, but he never knew where he was.

Plasticity is pervasive and crucialThe brain changes throughout our entire life because we're constantly seeing things we've never seen before.

We've only had written language for a small part of human history, so our brains are not genetically programmed to read. When we learn to read, a part of our brain must rewire and become devoted to recognizing words and letters. This adaptability doesn't stop when we're young; you can learn to read at any age. A researcher in China found a group of illiterate Chinese speakers in their forties. Initially, when he scanned them in an fMRI, their brains didn't respond to Chinese characters. After he taught them to read, their brain activity was identical to Chinese speakers who learned to read when they were young.

Sinha described the changes which take place when a child who is born with cataracts has them removed. From birth, "They see the world as if looking through a ping-pong ball that's been cut in half; they are looking through clouds. After surgery, we can see the mistakes that their brain makes as it learns to see." Someone who has seen all their life will recognize the edges of an object. For these patients, a basketball cannot be separated from its shadow initially, but over time they can learn to see edges. "We used to think that the brain was fully formed after 2-3 years of age, but we now know that development occurs throughout life."

The limits of plasticityAt the same time, there are critical periods for development. If the brain doesn't receive exposure during these times it can never learn to respond in the typical way. In terms of visual rescue, the earlier you can start it, the better the outcome will be. If someone's eyes aren't properly aligned at the age of 3 or 4, they will never see the world in three-dimensions; it will always be flat.

Analysis and Future DirectionsArtists have been performing tests on the visual system for years. They are doing experiments on our perception. A glance at a Picasso demonstrates just how much you can distort reality but still recognize it. By understanding vision, we'll know what makes these pieces of work so powerful.

We've uncovered some important properties of the visual system, but many more characteristics elude us. Ted Adelson suggests that we won't fully understand the computations that take place in the visual system until we can recreate them. "When we can program a machine to see as well as a human, then we'll understand human sight."

The brain is not static, so it's important to understand how it works at different stages of our life. In addition to mapping out the mature visual system, we need to know how the brain gets there. Sinha believes that when we understand that, we can help patients develop proper vision even if they get a late start in life.

Our senses are important, because they inform our actions. Seeing the world allows us to interact with it.

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Comment anonymously, call yourself whatever you want. Email addresses are strictly confidential, and providing one is optional (but will allow you to be notified of others’ responses and to dialogue immediately if you wish). This blog was viewed over a half a million times. For the public to be aware of procedural abuses, it has to hear about them. The blog author’s own story is here. Civility is the only constraint upon your speech.

The WSJ Law Blog: 2006-2017
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More than a decade ago, The Wall Street Journal launched Law Blog. It had a
simple name but a novel approach to legal coverage in the pre-Twitter era.
The ...

8 months ago

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