text:
# The QLIM Procedure

### Limited Dependent Variable Models

Subsections:

#### Censored Regression Models

When the dependent variable is censored, values in a certain range are all transformed to a single value. For example, the standard tobit model can be defined as

where . The log-likelihood function of the standard censored regression model is

where is the cumulative density function of the standard normal distribution and is the probability density function of the standard normal distribution.

The tobit model can be generalized to handle observation-by-observation censoring. The censored model on both of the lower and upper limits can be defined as

The log-likelihood function can be written as

Log-likelihood functions of the lower- or upper-limit censored model are easily derived from the two-limit censored model. The log-likelihood function of the lower-limit censored model is

The log-likelihood function of the upper-limit censored model is

#### Types of Tobit Models

Amemiya (1984) classified Tobit models into five types based on characteristics of the likelihood function. For notational convenience, let denote a distribution or density function, is assumed to be normally distributed with mean and variance .

Type 1 Tobit

The Type 1 Tobit model was already discussed in the preceding section.

The likelihood function is characterized as .

Type 2 Tobit

The Type 2 Tobit model is defined as

where . The likelihood function is described as .

Type 3 Tobit

The Type 3 Tobit model is different from the Type 2 Tobit in that of the Type 3 Tobit is observed when .

where .

The likelihood function is characterized as .

Type 4 Tobit

The Type 4 Tobit model consists of three equations:

where . The likelihood function of the Type 4 Tobit model is characterized as .

Type 5 Tobit

The Type 5 Tobit model is defined as follows:

where are from iid trivariate normal distribution. The likelihood function of the Type 5 Tobit model is characterized as .

Code examples for these models can be found in Types of Tobit Models.

#### Truncated Regression Models

In a truncated model, the observed sample is a subset of the population where the dependent variable falls in a certain range. For example, when neither a dependent variable nor exogenous variables are observed for , the truncated regression model can be specified.

Two-limit truncation model is defined as

The log-likelihood function of the two-limit truncated regression model is

The log-likelihood functions of the lower- and upper-limit truncation model are

format: plain


text:
First-Order Interpolation and Interpolating Proof Systems

16 pagesPublished: May 4, 2017

Abstract

It is known that one can extract Craig interpolants from so-called local
proofs. An interpolant extracted from such a proof is a boolean
combination of formulas occurring in the proof. However, standard complete
proof systems, such as superposition, for theories having the interpolation
property are not necessarily complete for local proofs: there are formulas
having non-local proofs but no local proof.

In this paper we investigate interpolant extraction from non-local refutations
(proofs of contradiction) in the superposition calculus and prove a number
of general results about interpolant extraction and complexity of extracted
interpolants. In particular, we prove that the number of quantifier alternations
in first-order interpolants of formulas without quantifier alternations is
unbounded. This result has far-reaching consequences for using local proofs
as a foundation for interpolating proof systems: any such proof system should
deal with formulas of arbitrary quantifier complexity.

To search for alternatives for interpolating proof systems, we consider several
variations on interpolation and local proofs. Namely, we give an algorithm for
building interpolants from resolution refutations in logic without equality and
discuss additional constraints when this approach can be also used for logic
with equality. We finally propose a new direction related to interpolation via
local proofs in first-order theories.

Keyphrases: interpolation, Resolution Calculus, superposition

In: Thomas Eiter and David Sands (editors). LPAR-21. 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 46, pages 49--64


text:
# Interface (2P-G)

Two-phase fluid and gas network interface

• Library:
• Simscape / Fluids / Fluid Network Interfaces

## Description

The Interface (2P-G) block represents a flow connection between a two-phase fluid network and a gas network. Pressure, temperature, and mass flow rate are equal at the interface. The fluid properties of each fluid network are not transmitted across the interface. To conserve fluid properties, ensure that fluid properties blocks on either side of the interface block have the same network properties.

The fluid on the two-phase fluid side must be superheated. If the fluid vapor fraction at the two-phase fluid port falls below `1` during a simulation, the block will return an error.

### Mass and Momentum Balance

Mass is conversed through the block:

`${\stackrel{˙}{m}}_{2P}+{\stackrel{˙}{m}}_{G}=0,$`

where:

• ${\stackrel{˙}{m}}_{G}$ is the mass flow rate at port G.

• ${\stackrel{˙}{m}}_{2P}$ is the mass flow rate at port 2P.

The internal and port pressures are equal:

`${P}_{G}={P}_{I}={P}_{2P}.$`

### Energy Balance

The temperature is maintained between the two fluid ports. The energy balance over the interface is calculated as:

`${\Phi }_{G}+{\Phi }_{2P}={\stackrel{˙}{m}}_{G}\left({h}_{I,G}+\frac{{w}_{I,G}^{2}}{2}\right)+{\stackrel{˙}{m}}_{2P}\left({u}_{I,2P}+{p}_{I}{v}_{I,2P}+\frac{{w}_{I,2P}^{2}}{2}\right),$`

where:

• ΦG is the energy flow rate at port G.

• Φ2P is the energy flow rate at port 2P.

• hI,G is the specific enthalpy of the gas at the internal node I.

• pI is the pressure of the fluids at the internal node I.

• vI,G is the specific volume of the gas at the internal node I.

• uI,2P is the specific energy of the two-phase fluid at the internal node I.

• vI,2P is the specific volume of the two-phase fluid at the internal node I.

• wI,2P is the speed of the fluid on the two-phase fluid side at internal node I:

`${w}_{I,2P}=\frac{{\stackrel{˙}{m}}_{2P}{v}_{I,2P}}{S},$`

where S is the value of the Cross-sectional area at ports 2P and G parameter.

• wI,G is the speed of the fluid on the gas side at internal node I:

`${w}_{I,G}=\frac{{\stackrel{˙}{m}}_{G}{v}_{I,G}}{S}.$`

## Ports

### Conserving

expand all

Entry or exit port to the two-phase fluid network.

Entry or exit port to the gas network.

## Parameters

expand all

Cross-sectional area of the thermal liquid and two-phase fluid ports.


text:
Derivatives problem

• Jul 15th 2007, 06:51 PM
starswept
Derivatives problem
Hello, back again with another derivatives question:

A grocery store determines that after t hours on the job, a new cashier can ring up N(t) = 20 - (30
÷
√(9 + t^2)

items per minute. Find N' (t), the rate at which the cashier's productivity is changing.

I've solved the derivative to

(9 + t^2)^(1/2) - 30 t
÷
(9+t^2)^(3/2)

But the correct answer should be simply

30 t
÷
(9 + t^2)^(3/2)

I have no idea how the (9 + t^2)^(1/2) in the numerator vanishes, though I've tried re-doing it several times. I'd greatly appreciate it if anyone could show me the steps to simplifying this derivative. Thank you in advance!
• Jul 15th 2007, 06:56 PM
topsquark
Quote:

Originally Posted by starswept
Hello, back again with another derivatives question:

A grocery store determines that after t hours on the job, a new cashier can ring up N(t) = 20 - (30
÷
√(9 + t^2)

items per minute. Find N' (t), the rate at which the cashier's productivity is changing.

I've solved the derivative to

(9 + t^2)^(1/2) - 30 t
÷
(9+t^2)^(3/2)

But the correct answer should be simply

30 t
÷
(9 + t^2)^(3/2)

I have no idea how the (9 + t^2)^(1/2) in the numerator vanishes, though I've tried re-doing it several times. I'd greatly appreciate it if anyone could show me the steps to simplifying this derivative. Thank you in advance!

Look at it this way:
$N(t) = 20 - \frac{30}{\sqrt{9 + t^2}}$

$N(t) = 20 - 30 \cdot (9 + t^2)^{-1/2}$

Now just apply the chain and power rules:
$N^{\prime}(t) = -30 \cdot -\frac{1}{2}(9 + t^2)^{-3/2} \cdot 2t$

$N^{\prime}(t) = 30t \cdot (9 + t^2)^{-3/2}$

$N^{\prime}(t) = \frac{30t}{(9 + t^2)^{3/2}}$

-Dan


text:
# How is it possible to electroplate using an Al3+ solution, when water is a stronger oxidant?

Suppose that I wanted to electroplate Al(s) onto a Cu(s) Cathode, (using an Aluminium Nitrate solution and Al(s) anode).

At standard conditions, Al(s) is the strongest reducing agent, which is good. However, H2O (l) is a stronger oxidising agent than Al3+, which should mean that no Al3+ can be reduced to form the coating on the cathode.

Despite this, I have seen several experiments achieve such an electroplating (with a solution, not molten).

How is this possible?

• Can you link to those experiments because this is very unlikely, unless they have cracked the code of making a solution of Al3+ with very high activity. – Nisarg Bhavsar May 22 at 7:34
• @NisargBhavsar core.ac.uk/download/pdf/11725439.pdf. Experiment F. I’m trying to replicate this experiment with oxidation state of 3+, and Al3+ is the only one that I can think of that can reduce directly to solid. Maybe there is another metal that could work – Simplex1 May 22 at 7:37

No ! It is not possible to deposit aluminum by electrolysis of a water solution. It may be done in a solution of $$\ce{AlCl3}$$ in an organic solvent like toluene, but not in water. And even in toluene, the conductivity is low. Metallic aluminum reacts with water, when this metal is not protected by an outer layer of aluminum oxide $$\ce{Al2O3}$$ as it is as soon as an aluminum piece is in contact with air.

For those who doubt about this reaction, let me add a few words. The reaction ion Al + H2O is not really violent, but it is visible. The only way of seeing this reaction is to prevent the alumina layer to cover the surface of the metal. And the only way of preventing this phenomena, is to dip a piece of metallic aluminum into an aqueous solution of mercuric chloride $$\ce{HgCl2}$$. In this case, the ions $$\ce{Hg^{2+}}$$ are able to cross the alumina layer and react with aluminum according to : $$\ce{2 Al + 3 Hg^{2+} -> 3 Hg + 2 Al^{3+}}$$ This reaction produces the appearance of some atoms of metallic mercury which form an amalgam with aluminum. Here the alumina layer is immediately formed but it does not cover entirely the metallic surface of aluminum. So the layer of alumina is not air proof or waterproof. So the corrosion continues. If the wet piece of aluminum is removed from the $$\ce{HgCl2}$$ solution, dried and deposited somewhere on a table, the alumina is formed steadily making sorts of white filaments that are growing before one's very eye. In a couple of minutes these filaments look like a delicate beard and measure several centimeters long. This phenomena stops when the fist layer of aluminum atoms is oxidized, because the mercury atoms are also eliminated. And the next oxidation of the aluminum surface is entirely covered by alumina.

• I see. I’m currently doing research on oxidation states, and metals which ions of 3+ oxidation states seem few and far between. I suppose the report I read failed to mention any additional solutions used. – Simplex1 May 22 at 7:21
• "Metallic aluminium reacts violently with water" I highly doubt that, I have seen aluminium chips from cutting aluminium pieces come into contact with water, and nothing has happened. At best, it will tarnish slowly. – S R Maiti May 22 at 9:29
• You can buy gallium aluminum “amalgam” and use it to generate hydrogen gas by putting it into water. Very expensive hydrogen generation, but same principle as with mercury: breach the aluminum oxide coat and reactivity happens! I upvoted, by the way. – Ed V May 22 at 20:11
• @EdV Thank you for for the information about the alloy Al-Ga, the I did not know. – Maurice May 23 at 9:47


text:
Mathematics

# $\displaystyle 96^{0}$ is an example of-

Obtuse

##### SOLUTION
obtuse angles are those angles which are greater than 90 degrees and less than 180 degrees..
so,96 degrees is an example of obtuse angle..

You're just one step away

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Single Correct Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87

#### Realted Questions

Q1 TRUE/FALSE Medium
A point  $D$  is on the side  $B C$  of an equilateral triangle  $ABC$  such that  $D C = 1 / 4$  $B C .$  then $( A D ) ^ { 2 } = 13 ( C D ) ^ { 2 }$
• A. False
• B. True

Asked in: Mathematics - The Triangle and Its Properties

1 Verified Answer | Published on 23rd 09, 2020

Q2 Single Correct Medium
Mark the correct alternative of the following.
In figure, if AB$||$CD then $x=?$
• A. $39$
• B. $44$
• C. $64$
• D. $54$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q3 Single Correct Medium
In an equilateral triangle, the incentre, the orthocentre and the centroid are
• A. collinear
• B. concyclic
• C. none of these
• D. coincident

Asked in: Mathematics - The Triangle and Its Properties

1 Verified Answer | Published on 23rd 09, 2020

Q4 Single Correct Medium
Find the values of the unknowns $x$ and $y$ in the figure (i).
• A. $x=60, y=70$
• B. $x=50, y=70$
• C. $x-50, y=60$
• D. $x=70, y=60$

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020

Q5 Subjective Medium
Read the following two statements which are taken as axioms:
(i) If two lines intersect each other, then the vertically opposite angles are not equal.
(ii) If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $180^0$.
Is this system of axioms consistent? Justify your answer.

Asked in: Mathematics - Lines and Angles

1 Verified Answer | Published on 09th 09, 2020


text:
# The value range for std of movie ratings?

For a movie rating, we can have its distribution like this:

Each rating would have a percentage. Consequently, we can obtain the mean, std from this distribution.

The question is what is the value range for the mean - std for the movie ratings?

Obivously, its bounded, and the std would be 0 for mean rating at 10. For 5.5 rating, the upper limit of std would be around 4? (given the extreme case that 50% for 10 and 50% for 1). And it should be centered around 5.5.

My questions are that:

1. Is there any distribution for the mean - std for such distribution?

2. How can I obtain the value range, in Python? (I can probably obtain it through generating random values and then calculate the mean and std. but it's a little bit hard to do it from scratch.)

UPDATE:

My simulation result:

Let's let $X$ be a random variable for the movie rating. Let's represent the probability distribution over $X$ as a vector $p$ s.t. $p_x = P(X = x)$. Let's let $f(p)$ be mean - std as a function of $p$. This gives us $f(p) = \sum_{x=1}^{10}xp_x - \sqrt{\sum_{x=1}^{10}(x - \sum_{x=j}^{10}xp_x)^2}$. We're looking for the range of values that mean - std can take for different probability distributions. This is equivalent to finding the minimum and maximum value of $f(p)$ under the constraint that $p$ represents a valid probability distribution. More precisely, we want:
$\min_p f(p)$ s.t. $\sum_{x=1}^{10}p_x = 1$ and $\forall x$, $p_x \geq 0$, which is the minimum value that mean - std can take, and we want $\min_p -f(p)$ s.t. $\sum_{x=1}^{10}p_x = 1$ and $\forall x$, $p_x \geq 0$, which is the max value that mean - std can take.
These are both examples of constrained optimization problems and can be solved in python using minimize from scipy.optimize. However, this may not give the correct minimum if $f(p)$ is not convex and may not give the correct maximum if $-f(p)$ is not convex.
• I now thinks that I can use Dirichlet distribution to simulute the rating distribution, and then calculate the mean - std relationship. – cqcn1991 May 24 '17 at 4:16


text:
QUESTION

# In 1200-1500 words, please address the following prompt: Which theory of free will (hard determinist, compatibilist, libertarian) do you find most convincing? Or, like William James and the Existentia

In 1200-1500 words, please address the following prompt: Which theory of free will (hard determinist, compatibilist, libertarian) do you find most convincing? Or, like William James and the Existentialists, do you find that we need to believe in freedom for practical purposes of guilt and responsibility? Be sure to engage at least two figures from our textbook.

No outside sources beyond the textbook are needed, but please be sure to cite any source you use in a works cited or in footnotes, including the textbook (remember to cite by chapter and section, e.g. Chaffee 4.2, since we don't have page numbers in the online text). Excellent papers will have grammatical and stylistic quality, factual accuracy, a clear thesis and evidence for one’s claim, and citations. Each paper counts for 10% of the final grade.

Tutor has posted answer for $10.00. See answer's preview$10.00


text:
## How to Use Nmap Command

By | 2016-09-08T18:31:03+00:00 September 8th, 2016|

Network Mapper is an open security tool used for network exploration, security scanning and auditing.  The nmap command includes plenty of options which make the utility much more efficient, but difficult for new users. Nmap are commonly used for: 1) Security audits 2) Multiple systems and network administrators find it useful for routine tasks such [...]

## Common Network Protocols and Their Ports

By | 2016-08-04T17:00:40+00:00 August 4th, 2016|

There are many protocols while establishing a connection in the internet. According to the type of connection need to be established, the protocols used varies. The protocols define the characteristics of the connection. Let’s see what a protocol is.   Network Protocol Simply, a protocol is a set of rules. A network protocol is a [...]


text:
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# Preparing for the next plague

Whether pan-vaccines or antibodies, SARS-CoV-2 is adding impetus to the race for broad-spectrum countermeasures against the world’s next infectious scourges.

In September, US president Joe Biden announced a plan to prepare for the next pandemic, with an initial outlay of $15 billion and a total investment of$65.3 billion over the next 10 years. The first goal is to “design, test, and approve a safe and effective vaccine against any pathogenic human virus within 100 days following the identification of an emergent viral pandemic.” A series of steps are laid out to accomplish this, the first being to characterize a so-called prototype pathogen from each of 26 viral families known to infect humans, to help identify potential epitopes that could inform vaccine design.

Pandemic preparedness is hardly a new idea. The most recent of many such efforts was the Obama administration’s pandemic playbook in 2016, following outbreaks of Ebola in West Africa and Zika in the Americas. In addition, the US National Institutes for Autoimmunity and Infectious Disease (NIAID) and the US Defense Advanced Research Projects Agency (DARPA) have had their sights on creating countermeasures that could be deployed quickly in the event of any outbreak. The speed with which the COVID-19 mRNA vaccines were developed was not an accident, but can be traced back to work funded and directed by both agencies. Yet the success of the present vaccines was also somewhat serendipitous, as coronaviruses have a particularly easy target in their spike (S) protein, not to mention having been the subject of more than a decade of research after the SARS-CoV-1 outbreak in 2002 and Middle Eastern Respiratory Syndrome (MERS) in 2015. In the next pandemic, the world may not be so lucky.

So with a combination of optimism and fear—optimism that a fast response is possible and fear that the next pathogen might not succumb so easily—pandemic preparedness has taken on a renewed urgency, which hopefully won’t dissipate once the current pandemic ends.

## Vaccines 2.0

The teams working on mRNA vaccines for SARS-CoV-2 are already turning their attention to the next pandemic. They are trying to leverage the knowledge gained from the successes of first-generation SARS-CoV-2 vaccines for the next set of pandemic vaccines.

One advantage of the mRNA vaccine platform, according to Moderna’s CSO Andrea Carfi, is that different mRNAs can be combined to target more than one pathogen or, in the case of SARS-CoV-2, more than one variant. Moderna has already announced that it has preclinical data on a combination flu and COVID-19 vaccine, which will be going into clinical trials next year, and it has plans for multivalent vaccines against SARS-CoV-2 variants beta and delta. There is no limit to the number of RNAs that can be combined, says Carfi. Moderna also has a cytomegalovirus (CMV) vaccine about to enter phase 3 trials that has six mRNAs, and has preclinical data on another comprising 10 mRNAs. Understanding how these mRNA cocktails give rise to an immune response is something the company is still working on. What its researchers can say is that they have tested multivalent vaccines encoding different proteins, and they can detect antibodies against the individual proteins. When it comes to timing, Carfi thinks they can go faster even than with their SARS-CoV-2 mRNA vaccine (which took 63 days from sequence selection to trial) by optimizing manufacturing and clinical readiness.

Given that the SARS-CoV-2 vaccine constituted the first experience of putting this type of vaccine in peoples arms on a global scale, safety had to be prioritized. But now, with hundreds of millions of people vaccinated, Carfi speculates that the US Food and Drug Administration (FDA) may have more confidence and familiarity with the platform, which could shave some time off the regulatory review process in future as well.

Ralph Baric’s group at the University of North Carolina has been collaborating with the leading mRNA research groups from University of Pennsylvania, NIAID and Duke University. Their next-generation vaccine is a chimeric mRNA vaccine that builds on the modular nature of the coronavirus S protein. According to David Martinez, a postdoc in Baric’s group since 2018, “The idea is to design a spike that instead of being monomorphic and eliciting immunity to one virus, you could increase the immunogenicity by having coverage for three viruses within one spike.” This is possible because there are three sites that are the targets of protective antibodies—the N-terminal domain, the receptor-binding domain (RBD) and the S2 domain. In a study published in Science, the Baric group report on a set of four different chimeric mRNA vaccines with different combinations of N-terminal domain, RBD and S-protein mRNAs and show they can raise high levels of neutralizing antibodies against multiple sarbecoviruses (the subgenus of coronaviruses encompassing SARS-1 and SARS-2). A vaccine with only the SARS-CoV-2 S protein vaccine did not show the same breadth. One chimeric vaccine, however, raised antibodies against SARS-CoV, SARS-CoV-2, the SARS-CoV-2 beta variant and two bat coronaviruses (CoVRsShC014 and Cov1-WIV-1) that are thought to be poised for human emergence because they can replicate well in human primary airway cells. Although the level of antibodies was lower than with a monovalent vaccine, the breadth of coverage was greater.

Another way of going for breadth is to vaccinate with virus-like particles (VLP). According to Adam Simpson, CEO of Icosavax, a spinout from the University of Washington’s Institute of Protein Design, “A VLP will inherently have a breadth of response that’s different [from] a soluble protein whether it’s made from a mRNA or not,” However, not all viruses can be made into VLPs, and Icosavax’s magic has been in using a computationally designed two-component system developed at the university, where any antigen can be displayed in an immunogenic array. The two components comprise proteins that are made separately and, when combined, self-assemble into a 128-subunit particle (VLP) with multifaceted icosahedral symmetry (imagine a soccer ball). The antigen (in the case of SARS-CoV-2, the RBD) is linked to one of the proteins via a linker comprising 8, 12 or 16 glycine and serine residues. “The reason it’s so important,” says Simpson, “is that it is a platform where we can put any antigen we want onto the VLP, and as components are proteins, they can be made by anyone with the technology for manufacturing proteins.” In their case, the antigen is made in a mammalian cell line (CHO cells) so that it’s properly glycosylated, and the second component in Escherichia coli because it’s inexpensive. “If you can make a protein, you can make our vaccine,” Simpson says.

Although other mRNA and protein nanoparticle vaccines are multiplexing to get breadth of protection, Simpson thinks that won’t be necessary with their VLPs. “If they look and smell like viruses, the body will react,” he says. In 2020 preclinical work with a SARS-CoV-2 VLP displaying 60 RBDs, conducted at the University of Washington, Neil King’s group found the VLPs not only produced tenfold higher titers than the S protein (a version engineered to stabilize the protein in the form it has before fusing with a cell it infects, employed in COVID vaccines) but also targeted multiple epitopes, suggesting that it would be hard for the virus to mutate around the VLP vaccine, which protects against related strains not in the vaccine. With a $10-million grant from the Gates Foundation and a partnership with Amgen, which is providing one of the protein components of the SARS-CoV-2 VLP, Icosavax has advanced VLP IVX-3441 into a phase 1/2 clinical trial in Australia. A different VLP provided by University of Washington researchers is being tested in clinical trials by SK Bioscience. Also at the University of Washington, David Veesler’s group, which participated in the discovery work behind some anti-SARS-CoV-2 monoclonal antibodies being developed by Vir Biotechnology as well as Icosavax’s VLP, continues to investigate how understanding of the basis of immunity to infectious agents can be used to guide vaccine design. In recently published work from his group, multivalent, mosaic VLPs and cocktails of different RBD VLPs raised neutralizing antibodies against a range of coronavirus variants and protected mice in challenge experiments with SARS-CoV-1, even when the combination did not include its RBD (Fig. 1). Veesler calls this an example of a second-generation vaccine, vaccine 2.0, which would be broadly neutralizing for multiple variants of SARS-CoV-2 and other sarbecoviruses. Vaccine 3.0 would be for beta-coronaviruses, which encompasses multiple lineages of which sarbecoviruses are only one. This is a long way off, however, due to the large diversity in the family, says Veesler. “I’m careful not to use the term pan-sarbecovirus. There are reasons for that: there’s a lot of diversity among known sarbecoviruses and we know that we might have only scratched the surface. There are so many that we have not yet discovered.” ## Accelerated aspirations The Coalition for Epidemic Preparedness Innovations (CEPI) aims to accelerate the development of vaccines against emerging infectious diseases. Part of its rationale is to counter the boom-and-bust cycle of commercial development programs, which receive an influx of funding at the outset of an outbreak but historically run out of funding when the epidemic threat recedes. The CEPI was launched at Davos in 2017 after the Ebola epidemic in West Africa had killed >11,000 people; here, again, vaccine development came too late to save any lives (Fig. 2). Since its founding, the CEPI has supported a number of innovative vaccine programs, as well as some conventional ones. In response to the current epidemic, the group has put$200 million dollars on the table to start the race towards broadly protective vaccines both against SARS-CoV-2—this call ended in September, and applications are under review—and one for beta-coronaviruses (the family that encompasses MERS as well as SARS viruses) more generally, which closed on 1 October 2021. “There’s an awful lot of room for improvement, not just stability, which has been well covered in the media, but also the productivity, driving down the costs, improving the safety profile and potentially improving the longevity of the response,” says Nick Jackson, the CEPI’s head of programs and innovations.

In the United States, DARPA recognized that traditional vaccine development timelines prevent vaccines from being an effective countermeasure in a sudden outbreak. In 2012, it launched a five-year program, ADEPT-PROTECT (Autonomous Diagnostics to Enable Prevention and Therapeutics), to develop alternative technologies. Initially this set out to explore nucleic-acid-based therapies rather than the more traditional types based on inactivated viruses or recombinant protein subunits. In fact, the first clinical trial using a systemically administered mRNA-based therapeutic encoding a secreted protein, Moderna’s monoclonal antibody (mAb) to chikungunya virus, was developed with DARPA backing (the company funded its phase 1 trial). The research behind that therapy came from another DARPA-supported group, Vanderbilt’s Vaccine Center, which is directed by James Crowe. Crowe’s group isolated potent neutralizing antibodies from a previously infected person, from which they determined the genetic sequence, which was used as the template for the mRNA-encoded antibody. Using the same approach, Crowe’s group has produced other protective antibodies, among them a cocktail of antibodies that inactivates Ebola virus and an antibody against Zika virus. In September 2019, Moderna reported phase 1 clinical trial results of its chikungunya therapy. A few months later, they, along with the rest of the world, turned their attention to SARS-CoV-2.

In March 2020, a mere 63 days after the company received the sequence of SARS-CoV-2, a Moderna mRNA vaccine, mRNA 1273, developed in partnership with the Vaccine Research Center at NIAID, became the first COVID-19 vaccine to enter clinical trials. This effort came about because of support from DARPA—a $25-million grant in 2003 to develop mRNA vaccines, followed by$56 million in 2020 to support manufacturing of the SARS-CoV-2 mRNA vaccine. DNA vaccine company Inovia was the second company to trial a nucleic-acid-based COVID-19 vaccine, in April 2020, with backing from the Bill and Melinda Gates Foundation and DARPA. After some fits and starts (the FDA imposed a clinical hold due to problems with the device used to deliver the DNA), this vaccine (INO-4800) received authorization to conduct phase 3 trials in Mexico and the United States.

## Antibodies as first responders

In 2017, as the ADEPT program was winding down, a follow-on program was spawned, the Pandemic Prevention Platform or P3. This program set up a challenge: to produce a protective antibody against a virus within 60 days of receiving a sample. According to P3’s program manager, Amy Jenkins, “We envisioned that the likely approach would be a nucleic-acid-based antibody that would be similar to vaccines. It would deploy as an RNA-based antibody, which would turn the body into a bioreactor.” Four teams took up the challenge: AbCellera Biologics, MedImmune/AstraZeneca, Duke University and Crowe’s group at Vanderbilt University.

The groups practiced on various viruses, but then in 2019, halfway through the program, they were confronted with the real-life challenge of SARS-CoV-2. Crowe says that he and Jenkins contemplated whether they were ready to tackle this, especially as, early on, patient samples were unavailable. But as soon as a US patient was identified in January 2020), they decided to go for it. The first step—identifying an antibody—was achieved in roughly a week by AbCellera, followed by Vanderbilt. As AbCellera’s CEO Carl Hansen described it, “We screened ~6 million B cells to identify ~500 unique antibodies that bound to the spike protein within a week.”

As part of the P3 program, AbCellera had participated in a couple of capability demonstrations—pressure testing—that were critical leading up to the pandemic. “It allowed us build relationships and to figure out all the weak spots in handoffs and communication,” says Hansen. Similarly, Vanderbilt’s group had done a full Zika sprint in 78 days and was partway through sprints for an H3N2 and an H1N1 antibody when they pivoted to SARS-CoV-2. With lessons learned from these first two sprints, they went from receipt of convalescent patient blood sample in March 2020 (from individuals who had been infected in Wuhan, China, in December 2019) to the transfer of antibody sequences for validated potently neutralizing antibodies to AstraZeneca in 25 days.

At that point, Jenkins felt that technology for using nucleic acid vectors to deliver the mAbs was not far enough along in development to make an mRNA-encoded mAb at the scale required for an already out-of-control pandemic. “The more sure bet in the spring of 2020 was to take the antibodies into more traditional platforms. So that’s what we did.” AbCellera Biologics teamed up with Eli Lilly (which was not receiving P3 funding); and in May 2020, just 91 days after receiving the patient sample, they dosed their first patient. “They didn’t hit 60 days, but we were only half way through the program,” says Jenkins. Lilly received an Emergency Use Authorization (EUA) for bamlanivimab (a humanized IgG1 with modified Fc regions) for treating patients with mild to moderate COVID-19 in November 2020. “The encouraging thing was that they were quickly discovered, and among the first interventions along with remdesivir and some steroids—encouraging that we could deploy so rapidly, being honest, and surprised that protein-based manufacturing was quick,” she says. Hansen gives credit to their partner, Lilly, for stepping up. “Lilly deserves tremendous credit for recognizing the opportunity. They haven’t traditionally been in infectious disease and they wanted to be a positive force in responding to COVID,” he says. Although the EUA for bamlanivimab as a monotherapy was revoked by the FDA in April 2021, it is still in use along with a second antibody, etesevimab, that Lilly licensed in from Shanghai Junshi Biosciences. Collectively these antibodies have been used to treat approximately 600,000 patients, according to Hansen. “The results have shown, if you look at the stats, [this] has probably saved tens of thousands of lives and tens of thousands of hospitalizations,” he says.

From their COVID-19 sprints, Vanderbilt isolated hundreds of SARS-CoV-2 antibodies and licensed two to AstraZeneca, which engineered them to extend the half-life and to eliminate potentially harmful effector functions. AstraZeneca took AZD7442, a combination of two long-acting antibodies, tixagevimab and cilgavimab, that block the SARS-CoV-2 S protein from binding to its host receptor angiotensin-converting enzyme 2 (ACE2), into clinical trials for prevention of COVID-19. Tixagevimab and cilgavimab are both human IgG1 mAbs engineered with five amino acid substitutions (at positions T240, M241, Y308, T310 and E312). In September, the company reported phase 3 clinical trial results on more than 3,000 at-risk (uninfected) people: the antibodies were 77% effective in preventing infection, making this the first mAb combination to demonstrate prevention of COVID-19—an important first in demonstrating a new way to enlist antibodies during a pandemic.

## Pain points

The P3 groups collectively demonstrated that antibodies can be isolated and deployed quickly, not just for treatment but also for prevention, and that this can be done even from scratch in a few months, faster than for typical vaccines. And although the RNA vaccines were also put into arms in amazingly short order, a vaccine-induced immune response can take weeks to months to develop. Furthermore, RNA vaccines may not work for all viruses nor for all people, such as those who are immunocompromised (by some estimates, as many as 15 million in the US alone). For tamping down an emerging potential pandemic, antibodies potentially provide a better solution to contain an outbreak in its early days, while vaccine development and production proceed.

Historically, however, only a few anti-infective antibodies have ever been developed and approved for use. Two decades separated the approvals of the first two marketed anti-infective mAbs: palivizumab in 1999 and bezlotoxumab in 2017. The former is a humanized IgG1κ mAb targeting an epitope in the A antigenic site of the respiratory syncytial virus (RSV) F protein; the latter is a human IgG1 mAb that binds Clostridium difficile toxin B

There are several reasons why such mAbs have not taken the world by storm. Much as for antibiotics, the commercial market for anti-infective antibodies has essentially failed. Most biotech companies working on mAb development have focused instead on more lucrative conditions in oncology, inflammatory disease or rare conditions. Any manufacturing base for an anti-infective mAb indicated for use in a pandemic must have the capacity to make antibodies for millions, or even billions, of people. Yet antibody manufacturing capacity, which typically uses mammalian (CHO) cells, is expensive and is finite worldwide. Even though the market is gargantuan, the high cost of goods for bulk manufacture of CHO cells means that anti-infective mAbs are not an attractive business proposition, as they have low product price points and low returns on investment. And the problems don’t stop there: antibodies also pose problems for distribution in limited-resource public health settings because they must be administered by intravenous infusion, which requires hospitals or infusion centers and trained personnel, which very often are absent in resource-poor countries.

Several antibody engineering biotechs have been chipping away at these issues and have already started clinical testing (or will soon) of mAbs as prophylactics. Centivax, through a combination of dry- and wet-lab techniques, has increased the mAb’s half-life, broadened its delivery modes, increased its potency and removed potential unwanted effector functions—enabling, among other things, intramuscular (i.m.) injections of small amounts of their antibodies, which simplifies their administration and potentially drives down cost. Centivax founder Jacob Glanville applied his decades-long study of antibody structure–function relationships to understanding the properties of populations of complementarity-determining region (CDR) mutations that are found on naturally occurring antibodies after surviving selection. The Centivax team combined that bioinformatics information with phage display, where they can apply multifactor selection for features like high-affinity mAb binders and the lack of self-protein–protein interactions to avoid viscosity problems, among other properties. Centivax will be taking its first product, CENT-B9 for SARS-CoV-2, into clinical trials later this year, with funding from US Naval Medical Research Center, which has an interest in prophylactic antibodies to stop infections from spreading throughout a ship.

Adagio Therapeutics, which was spun out of the antibody engineering company Adimab in 2020 to fight the pandemic, has an engineered fully human mAb that reacts with all known SARS-CoV-2 variants now in phase 2/3 trials for both disease treatment and prophylaxis. (Adagio is doing research and clinical development all on its own, having raised >$450 million in venture capital and$356 million in an initial public offering in 2021.) Tillman Gerngross, Adagio’s founder and CEO, took a gamble that the pandemic was not going to go away quickly and embarked on a program of antibody design that would capture all the known and potentially unknown variants of SARS-CoV-2. “We knew we weren’t going to win the race because it takes time to do all this engineering work. So from the beginning, we needed the best molecule with the expectation that it is going to be a longer haul and not just a pandemic that goes away, which is exactly how it played out,” he says. Adagio’s lead antibody, ADG20, was among a group isolated from a convalescent SARS-1 donor, and targets a conserved epitope on the S protein present on all SARS-1, SARS-2 and many potential emergent bat viruses. Using its antibody engineering platform, the company was able to retain breadth while improving binding affinity 500-fold and neutralizing capacity 70-fold. ADG20 is the only small-molecule-like intramuscular injectable mAb that has this breadth, covering all SARS-CoV-2 variants, at such high affinity, according to Gerngross.

Crowe, although he directs Vanderbilt’s vaccine center and is a believer in vaccines, thinks that i.m. delivery will be a game changer for the use of mAbs in prophylaxis (Table 1). The question is how long they will protect against illness. The AstraZeneca trial went for three months and stopped when people started getting vaccinated. Crowe notes that he has been saying for years that for flu, an antibody—specifically one with a half-life extension to ~90 days, enabling protection potentially for up to a year—would be a better alternative, as flu vaccines lose potency after a few months. “I get why people don’t like saying this out loud. But this type of antibody could work better and longer,” he says.

For pandemic preparedness, Herbert ‘Skip’ Virgin, executive vice president of research and CSO at the infectious disease company Vir Biotechnology, says: “What you want is an antibody that binds to as many of the viruses of a group as possible, that is insensitive to variation that’s occurring in a pandemic or historically, and that is potent at a low dose as you can only manufacture so much, as you want to save as many lives as you can. These are the properties that are going to make the difference between a truly exceptional pandemic preparedness antibody and everything else. That’s our philosophy, that’s what we do and we think we have the antibodies that do this.”

Vir’s first commercial product, sotrovimab—a human IgG1κ mAb engineered with an Fc domain of increased FcRn binding affinity that targets a conserved epitope on the SARS-CoV-2 S protein RBD—was granted full approval in Australia in August 2021, as well as EUAs in multiple countries. This mAb, derived from B cells of a patient who recovered from SARS-1 in 2003, targets an epitope on the S protein that is conserved in the sarbecovirus family. The antibody was engineered to extend its half-life, which, according to Virgin, providentially enhances distribution to the lung. Vir has a second mAb under development (VIR-7832) that in addition contains a mutation (with an Fc engineered to create M428L and N434S amino acid substitutions for increased human FcRn affinity) that has been shown in vitro to recruit effector functions. Virgin says that his team believes this offers the potential for the antibody to function as a T-cell vaccine, creating what they are calling dual-action antibodies. “This might not be the most popular way to word this—neutralization as a concept is easy to tell and easy to sell, but it’s not accurate. There is no biological system in which neutralization is the only correlate of the efficacy of an antibody against viruses,” he says. Sotrovimab is in trials now for i.m. administration, according to Bolyn Hubby, Vir’s chief corporate affairs officer, which she says will be a “huge milestone in transitioning away from i.v.”

More recently Vir researchers and collaborators have identified a number of antibodies with unique properties, among them broadly neutralizing activity targeting a cryptic epitope in the RBD, and a narrow escape profile (mutation scanning showed that only one substitution leads to escape).

There are two approaches to pandemic preparedness: create platforms that can quickly be deployed; or have a stock of broadly effective products on the shelf—antivirals, antibodies and vaccines. Several consortia are gearing up to do the latter.

Crowe’s group at Vanderbilt came up with the idea they call ‘Ahead 100’, with the goal of making best-in-class antibodies for each of 100 targets from among the 25 families of viruses that are pathogenic to humans, to take them through a phase 1 safety trial with good manufacturing practice (GMP) material and stockpile 10,000 doses. He calculates that getting to that point will take $25 million, so going beyond that for 100 antibodies is impractical for any single group. Instead, Crowe helped organize a consortium, the Global Pandemic Prevention and Biodefense Center—potentially a$2.5 billion project—which launched on 11 August 2021 to take this idea forward. The organization is housed in what is called the Connected DMV—Washington, DC, Maryland and Virginia—where there is a concentration of federal agencies (NIH, FDA and Fort Detrick) and pharmaceutical company headquarters (AstraZeneca, GlaxoSmithkline and Emergent BioSolutions). Crowe raised $2.5 million for the planning phase from the Gates Foundation, the CEPI, the US government and two commercial partners (Regeneron and Moderna). The consortium is looking for partners to put in$25 million per target in the first project: Advanced Human Epidemic Antibody Defenses 100 (AHEAD 100), which will be led by Crowe.

The CEPI is thinking along the same lines. It is launching what Jackson described as “a world-class effort to rank all the families according to their threat level, in the most sophisticated way possible, by tapping into crowd-sourcing virologists, experts who understand zoonotic spillovers capable of using models and computational elements to derive a definitive list for what are the greatest threats across the families we know.” Additionally, the coalition is working with a network of manufacturers to support the expansion of vaccine manufacturing capability around the world. “We want the regions to have equitable access and avoid the nationalisms and bilateral deals that have been problematic in this outbreak.”

And the alphabet soup of US agencies are seemingly keeping their focus on the threat. DARPA has a new program called ‘Nucleic Acids on Demand Worldwide’ (NOW), which is looking to develop mobile manufacturing capacities that can be located where the need is greatest, and potentially shorten the time to distribute vaccines and therapies. In October, the NIAID announced a \$36-plus-million-dollar program to develop pan-coronavirus vaccines, with funding going to three academic programs, located at the University of Wisconsin, Madison, Brigham and Women’s Hospital in Boston and Duke University in North Carolina. Recognizing the need for a comprehensive strategy, the funding is going to multidisciplinary groups with expertise in virology and immunology, immunogen design, and innovative vaccine and adjuvant platforms and technologies.

But preparing for the next coronavirus is not going to be enough. Nancy Sullivan, chief of the Biodefense Research Section at the NIAID, points out that even within a virus family, a single approach may not be a true prototype for the entire family. Her experience with filoviruses demonstrated this: “DNA vaccines protect against Marburg, but they don’t protect against Ebola.” What’s needed, she points out, is “building a knowledge base, in a rationale way, and trying to incorporate some flexibility, not focusing on the hundreds of viruses that exist but instead focusing on the immunological principles that underpin protection and building that toolbox to cover those different immunological pathways.” Something simple, such as the order in which you give prime and boost doses and the interval between them, can shape the immune response. “You can tune the immune response by adjusting one pair of vectors, which one you give first and the interval between the shots,” she says.

Jeffry Ulmer, a retired vaccine expert with experience at Chiron, Merck, Novartis and GlaxoSmithKline, worries that the SARS-CoV-2 vaccine success may be the exception, rather than the rule, for future pandemics. “We saw a spectacular success with [mRNA vaccines for] COVID-19 but pretty much everything else that was tried also worked, including DNA. It ought to give us some pause that this particular antigen is relatively easy, and that the next application of the technology could face a much more difficult task.”

Authors

## Rights and permissions

Reprints and Permissions

DeFrancesco, L. Preparing for the next plague. Nat Biotechnol (2021). https://doi.org/10.1038/s41587-021-01140-x


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# Is there a “small cap” version of greek symbols out there?

I need to use two versions of the Omega greek letter in the same equation, but I don't want to use uppercase and lowercase (as the latter looks like a w). Is there a way to differentiate between the two uppercase Omega characters (perhaps with an equivalent to small caps for latin characters)?

There's a text command in package tipa called \textscomega which seems to do what you want.

You can define

\newcommand{\scOmega}{\text{\textscomega}}

and use \scOmega in your document as in the following example:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tipa}

\newcommand{\scOmega}{\text{\textscomega}}

\begin{document}
\begin{equation*}
\Omega\neq\scOmega
\end{equation*}
\end{document}

Output

If you don't want to load the tipa package entirely, you can load fontenc with the option T3 (needed for tipa symbols) and declare

\DeclareTextSymbolDefault\textscomega{T3}

MWE:

\documentclass{article}
\usepackage{amsmath}

\usepackage[T3,T1]{fontenc}
\DeclareTextSymbolDefault\textscomega{T3}

\newcommand{\scOmega}{\text{\textscomega}}

\begin{document}
\begin{equation*}
\Omega\neq\scOmega
\end{equation*}
\end{document}


text:
# Scattering of Light

1. Jun 5, 2009

### Xian

I pretty much understand the idea of photon of some wavelength λ exciting an electron in atom above the ground state if the difference between the ground state and a higher energy level is exactly hc/λ. Not hard, but what happens to the electron and the atom when the photon energy is below the excitation energy? From what I've been reading in Optics by Hecht it seems that the photon will pass through the electron cloud and its electromagnetic nature will set the electron cloud into an oscillatory motion making it so the atom now behaves like an oscillating dipole (similar to those in radio towers). This oscillating dipole will then emit a photon of the same frequency as its oscillation (or the same frequency as the passing photon, or maybe coincidentally both, I'm not sure). What happens to the original photon however? Does it just continue to move on, gets weakened and moves on, or does it get absorbed by the cloud when it sets it into an oscillatory motion? I suppose conservation of energy would point to either the second or third option no?

Also, what happens when the photon is not carrying precisely the excitation energy, but more? Will the electron get promoted above ground level and then the atom absorbs the rest of the energy as just kinetic?

2. Jun 5, 2009

### fatra2

First of all, a photon does not weaken with time. Therefore, if the photon does not carry enough energy to excite the atom, then it will just carry on its way, like nothing happened.

If the photon carries more energy than what is needed for a one level excitement, the electron will be even more excited and "climb" the scale even higher. If the photon as more energy than what is "allowed" by the atom, the electron will simply leave the atom (process that is called ionizing an atom).

Cheers

3. Jun 5, 2009

### Xian

Hey thanks for the reply fatra, but I think I need to clarify myself a little.

In the first question when I said the photon weakens I meant that for instance the photon passes through the electron cloud, and as it does the oscillating electric component of the photon will cause the electron cloud to vibrate, so by conservation of energy the photons energy should be weaker since the atoms total energy has increased. This is what my textbook Optics by Hecht tries to illustrate. The only part that its not to clear on is what happens to the passing photon. I assume that it doesn't just fly on by like nothing happened, and so it either gets weakened by the transfer of energy (if thats possible) or gets completely absorbed by the electron cloud, though it does not excite the individual electrons, but instead is absorbed by the cloud in the sense that the cloud now oscillates. We could oscillate the cloud in a similar fashion by applying an external E-field. Also, even besides this, photons do weaken in certain situations such as the Cosmic Background Radiation of the universe. There the photons were once very energetic (since they were from the big bang) but then were weakened (though I'm not entirely sure what it was that weakened them, it would not just be distance alone but likely something from special or general relativity).

Also, for the second part, I meant to say that the photon has enough energy to excite the electron up one energy level, and has a just a little bit extra, not enough to make it climb higher, but enough so that there is a surplus of energy after that one electron gets bumped up. What happens if the photon has this much energy? My guess was that the whole photon gets absorbed, but the extra energy is absorbed as kinetic, though this doesn't feel right.

4. Jun 5, 2009

### Bob S

If you review the theory of Rayleigh scattering of sunlight in air, you will find that the theory is based on classical scattering of light waves (plane waves) off of uncharged atoms. Rayleigh scattering correctly predicts both the 1/lambda4 wavelength dependence (note:without any discrete transitions) and complete polarization (note: only with very smogless clear sky) of the scattered light at 90 degrees. The cross section (probability) for scattering is very roughly equal (within a factor of 32 pi/3) to the square of the classical electron radius (2.828 Fermi), therefore much smaller than atomic sizes (Bohr radius is 1372 x classical electron radius. So very roughly a visible photon "hitting" an atom has a very small chance of scattering.

5. Jun 5, 2009

### Xian

Though Rayleigh scattering is a useful to know and understand, I would like to understand as well as possible what goes on in the situation I mentioned above (which of course includes scattering). To really understand this though I will need to understand any quantum tricks that go on of course, and this is unavoidable to do the discrete nature of light and atoms. The classical picture of light as a wave is useful and more or less "accurate" when the number of photons is very large, however I'm looking for the best answer and that means looking at the single-photon-to-single-atom interaction. If possible I'd love to hear whatever you know in that area, and would greatly appreciate it.

6. Jun 7, 2009

### mn4j

Photons can and do transfer momentum to electrons and vice versa even when the energy of the photon is not sufficient to excite the electron. The photon will continue on it's way with the same energy but different momentum. The electron will be left with the same energy but different momentum as well.

7. Jun 21, 2009

### invisigo

I believe you are confusing yourself by mixing classical and quantum optics. Hecht's description uses classical optics, in which the atoms are dipoles and photons are EM waves that excite them. However, you cannot bring in the idea of "energy level" into this picture of light-matter interaction, because that is a quantum concept. In this description, yes, a low energy...and I really shouldn't even bring in the idea of energy, or even photon...let's say a low frequency EM wave has the potential to excite any atom (which is modeled as a dipole). The classical description is limited this way, because it can lead to incorrect deductions.

In the quantum description (or maybe even the semi-classical model), you can bring in the idea of energy levels. Now your whole model of physics changes. The atom is no longer a dipole, but an object with a bunch of energy levels. Throw away the dipole. I'm no expert (or even novice) in quantum electrodynamics, but I think your whole idea of electromagnetism changes too. But in any case, photons can be thought of as packets of energy, and if that energy does not match an atomic transition level, then it will pass through the atom.

8. Mar 24, 2011

I was under the impression that a photon is absorbed by the electron and excites it if the photon carries the minimum amount of energy to do so.
From what I've been taught, its an "all or nothing" process where the photon must have the minimum amount of energy or it simply won't affect the electron.

Also, when a photon of adequate energy excites an electron, I believe it is absorbed but is then re-emitted as soon as the electron falls back down to its original energy level. It is in this way that conservation of energy is preserved: a photon of equal energy is re-emitted. So, the photons being emitted in the atmosphere that are giving the sky its blue hue aren't actually the original photons, but the re-emitted ones.

This is what I can remember to the best of my abilities from class but I could be wrong. Someone please feel free to correct me if I am.

9. Mar 25, 2011

### Xian

Agreed, but my question is more about what happens below the threshold.

If the photon does not have enough energy to excite an electron beyond the ground state, my quantum intuition tells me that the photon would just pass through as if there was nothing there.

My classical (semi-classical?) intuition tells me however that since a photon is an electromagnetic oscillation that it should interact electromagnetically with the electrons (and protons) of the atom.

I know next to nothing about quantum electrodynamics but from what I get, an photon is described to be an excitation of the electromagnetic field... I'm not sure how to work with this interpretation (assuming it is a correct one).

Thoughts anybody?

10. Mar 26, 2011

### alxm

Right. Classically Rayleigh scattering is fairly intuitive in both pictures. As an electromagnetic wave, the atom is a polarizable 'medium', so you have diffraction. As particles, a photon simply scatters off the electron elastically. However your QM intuition is leading you wrong here; it's more classical than you might think. Consider what the atom's Hamiltonian looks like if you've got an external field - the electron has a coupling to the electrical field and so you have a response and polarization (Stark effect), even if the electron does not change states. So the classical wave picture more or less works here.

An alternate view (from QED) is that the photon is absorbed and that there's excitation to a virtual electronic level, followed by immediate re-emission. This is allowed because it's not actually real; the electron is never observed to be in that excited state. (It also means you don't have to worry much about selection rules) That as opposed to fluorescence, where the exited state is real.

11. Mar 26, 2011

### lightarrow

Anyway, if the photon does not have enough energy to excite an electron beyond the ground state, it's not correct to say that the photon "would just pass through as if there was nothing there": light *does* interact with the atom, just because it's scattered.

12. Mar 27, 2011

### johng23

My understanding of this process (From Boyd's "Nonlinear Optics") is that an electron could stay in a virtual level for a time $$\Delta$$t = h/$$\Delta$$E, where $$\Delta$$E is the energy difference between the virtual level and the nearest real level in the system. If that's a valid way to think of it, how can we say the re-emission is immediate? For example, with energy differences in fractions of an eV, the electron can stay in the virtual level for a few femtoseconds, appreciable compared to the duration of an optical cycle. So the re-emitted radiation would not be in phase.

13. Mar 28, 2011

### alxm

Because it is, the electron is not observed or observable in this virtual state, no measurable interactions occur or can occur between the absorption and re-emission.

By analogy to the ordinary uncertainty principle: You can measure the effects of an electron acting as if it were in two places at once, but we don't say it actually is in two places at once.

The system here is acting as if it'd been excited to a virtual level for that amount of time.

14. Mar 28, 2011

### johng23

I don't think I fully understand. If the re-emission is immediate, how is the system acting as if it were in the virtual level for the time $$\Delta$$t? What is the significance of this characteristic time?

15. Mar 28, 2011

### Antiphon

Johng23, you original question was about dielectric polarizability. This is not the same as electronic transitions, a much higher energy (and discrete) event.

You were asking how it is possible for a quantum to perturb a dipole and remain unaffected. The answer is that it does not remain unaffected. It is absorbed and reemitted with some probability by the dipole. Dielectric polarization is not a bound energy state with discrete states like an electronic orbit. A photon of nearly any energy can excite the dipole.

16. Mar 29, 2011

### lightarrow

Right. Using a metaphor, it's like hitting a ball which goes up a slope and then goes back because it doesn't find an equilibrium position at an higher altitude with respect to the ground.


text:
Welcome to mathimatikoi.org forum; Enjoy your visit here.

## An integral identity for Harmonic Functions

Partial Differential Equations
r9m
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### An integral identity for Harmonic Functions

If $u$ be a Harmonic Function in a open connected set $\Omega \subset \mathbb{R}^n$ and $\overline{B(x_0,R)} \subset \Omega$ (the closed ball of radius $R$ centered at $x_0 \in \Omega$).

(i) Show that: $$\int_{\partial B(0,1)} u(x_0 + ry)u(x_0 + Ry)\,d\sigma(y) = \int_{\partial B(0,1)} u^2(x_0 + cy)\,d\sigma(y)$$ where, $r \le c \le R$ and $c^2 = rR$.

(ii) Using the above identity show that if $u$ is locally constant, then it is constant in $\Omega$.

[$\partial B(0,1) \equiv S^{n-1}$ is the boundary of the unit ball in $\mathbb{R}^n$ and $\,d\sigma(y)$ is the surface measure on $\partial B(0,1)$].


text:
This is an archived static version of the original phylobabble.org discussion site.

# Best mechanism to report negative results

Alexis_RAxML

Dear All,

I was wondering what would be the best way to regularly publish negative results, since such work is not likely to be accepted anywhere and this is a problem for the community.

Maybe setting up some web-based resource might be a good idea. Is anybody else worried about this and looking for a good way to publish and more importantly, make available, negative results.

I have recently been trying to implement a simple heterotachous model in RAxML to resolve a hard phylogeny, but it doesn’t work at all. So where could I report this?

Alexis

mlandis

Is it frowned upon to publish this sort of technical autopsy to arXiv? Or perhaps to Figshare?

jgsumner

I would have thought it is fine to post such things to arxiv.

GrahamJones

From their title, it seems like the Journal of Negative Results - Ecology & Evolutionary Biology would be happy to hear from you.

I can’t think of a good reason why Biorxiv wouldn’t want to publish negative results, although at the moment articles are in three categories:

New Results is most appropriate for articles that describe an advance in a field.
Confirmatory Results should be selected if the findings largely replicate and confirm previously published work.
Contradictory Results should be selected if the studies largely replicate experimental approaches used in previously published work but the results contradict and/or do not support it.

Biorxiv is new, and perhaps they just need a nudge to include a 4th category.

funwithwords26

Hi Alexis, I think PLoS ONE ought to take it.


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I’m still a big fan of InfoBarrel, Eric, even though I haven’t been able to write much. With what I am earning there, I’ve actually shifted to outsourcing quite a bit of content…call it a “respite” from writing, I had just needed a break. Even if one pays $5-$10 per article, IF the keywords are researched properly and effectively, one can easily turn that one article and earn several hundred off of it in it’s lifetime. Right now, one of my friends had written a single article that, already this month, has earned over $83 on InfoBarrel. Not too shabby at all… Network marketing, or multi-level marketing, seems to be on the rise. Companies such as Young Living Oils, Avon, Pampered Chef, and AdvoCare are all multi-level marketing companies. You can earn passive income through network marketing by building a team underneath you (often referred to as a down line.) Once you have a large team you can earn commissions off of their sales without having to do much. Can you expound on the use of publicly-traded REITs as a passive income source? I’m 31 years old. No children. No wife. No dependents. (I am the closest thing to Ebenezer Scrooge you’ll ever see). My monthly expenses amount to less than$2,000 per month (most of which go to pay student loans) . I have a decent job making over $55K per year. I also have a$60K inheritance coming my way in a few weeks. I am absolutely crazy about achieving absolute financial independence, which for me would require a passive income of over $2000/month to cover my living expenses. I could achieve that in a mere couple of years if I were to save excessively and dump my savings (and inheritance) into a Mortgage REIT via the stock market, most of which are shelling out above 10% returns in dividend payments. Is this a good strategy for me? Or am I being too hasty and assuming too much risk? I need to create a passive income stream that has a definable risk profile.I have$250k cash as a safety net in my savings account getting a measily 40 bps but I am somewhat ok with this as it is Not at risk or fluctuation (walk street is tougher nowadays). i have 270k in equity in my house, thinking of paying off the mortgage but probably does make sense since my rate is 3.125 on a 30 yr. I have 275k in my 401(k) and another 45k in a brokerage account that is invested in stocks that pay dividends.
Currently we have a duplex and a condo that we rent out. I manage the properties myself so it does take a little time. The rental properties are mostly passive, but I have to do some work occasionally. Recently, I had a tree trimming company out to trim the maple in the back and remove some dead arborvitaes along the fence. We decided to replace the arborvitaes with potted bamboos to help screen the property. So this past weekend, we split a pot of bamboo and planted some mint in the garden. That one sentence sounded easy, but it took us 3 hours to do. We carted an old pot of bamboo from our balcony and it was a struggle. That thing must have weighed 100 lbs. Anyway, we’re willing to put some work into the duplex because we plan to relocate there at some point. Also, the rental income shows up as negative income in our tax due to depreciation. That’s a nice side benefit to being a landlord.
I see you include rental income, e-book sales and P2P loans as part of your passive income. Do you not consider your other internet income as passive? Is that why it’s not in the chart? Or did you not include it because you would rather not reveal it at this point? (I apologize if this question was already answered – I didn’t read through all the comments, and it’s been about a week since I actually read this post via Feedly on my phone)
One of the easiest ways to increase your passive income is to shift your savings to a bank that pays a higher yield on your savings — for example, Discover Bank and EverBank pay almost 1% for your money. Although it doesn’t sound like much (especially in this low interest environment), little things do add up and eventually interest rates will rise.
If you pay your bills with a credit card make sure it offers cash back rewards. You can let your rewards accrue for a while and possibly put the easy money you earned toward another passive income venture! (Be sure that the card you select doesn’t have an annual fee or you might be cancelling out your rewards). Check out this list of the best Cashback Rewards Cards.

For the 95% on $10 a day, see Martin Ravallion, Shaohua Chen and Prem Sangraula, Dollar a day revisited, World Bank, May 2008. They note that 95% of developing country population lived on less than$10 a day. Using 2005 population numbers, this is equivalent to just under 79.7% of world population, and does not include populations living on less than $10 a day from industrialized nations. If the income is for personal services performed partly in the United States and partly outside the United States, you must make an accurate allocation of income for services performed in the United States. In most cases, other than certain fringe benefits, you make this allocation on a time basis. That is, U.S. source income is the amount that results from multiplying the total amount of pay by the fraction of days in which services were performed in the U.S. This fraction is determined by dividing the number of days services are performed in the United States by the total number of days of service for which the compensation is paid. While stocks are terrific income producers, they can be volatile. Every few years, the stock market tends to stagnate or drop for a while before recovering, and that can be problematic if you were counting on your stocks having a certain value at a certain time. One way to lock in an income stream is by buying a fixed annuity (as opposed to variable or indexed annuities, which can have steep fees and overly restrictive terms). Annuity contracts will be more generous when interest rates are higher, but here's how much income they might deliver at recent rates: Blogs and authority websites are different than niche websites, because they generally imply on-going content generation. Sure, I could stop writing on this blog today and let it sit forever, but that’s not the intention of the blog. Furthermore, blogs and authority websites tend to include a community or social aspect. We have Facebook pages and Twitter accounts (can someone explain to me why the hell I haven’t made a Facebook page yet?), and we discuss various topics in the comments of each article or blog post. Although SEO does affect traffic, community is more important. These challenges are international in scope and are priorities for the Central Intelligence Agency. If you have information about these or other national security challenges, please provide it through our secure online form. The information you provide will be protected and confidential. The CIA is particularly interested in information about imminent or planned terrorist attacks. In cases where an imminent threat exists, immediately contact your local law enforcement agencies and provide them with the threat information. Enrollment in, or completion of, the H&R Block Income Tax Course is neither an offer nor a guarantee of employment. Additional qualifications may be required. Enrollment restrictions apply. There is no tuition fee for the H&R Block Income Tax Course. However, you may be required to purchase course materials. State restrictions may apply. Additional training or testing may be required in MD and other states. Valid at participating locations only. Void where prohibited. This course is not intended for, nor open to any persons who are either currently employed by or seeking employment with any professional tax preparation company or organization other than H&R Block. During the course, should H&R Block learn of any student’s employment or intended employment with a competing professional tax preparation company or service, H&R Block reserves the right to immediately cancel the student’s enrollment. The student will be required to return all course materials. CTEC# 1040-QE-0889 ©2018 HRB Tax Group, Inc.  # With passive income sources, you can go long periods of time without doing work, yet still earn income. In some cases, that income can expand without much additional input from you. For example, if I build a website in 5 hours and after a month, it has only made$50, my time to that point was worth $10/hour. It doesn’t stop there, however. In a year, if the site has earned$600, the value of those initial 5 hours grows to \$120/hour. As time goes on, that number can continue to grow indefinitely.

This equation implies two things. First buying one more unit of good x implies buying {\displaystyle {\frac {P_{x}}{P_{y}}}} less units of good y. So, {\displaystyle {\frac {P_{x}}{P_{y}}}} is the relative price of a unit of x as to the number of units given up in y. Second, if the price of x falls for a fixed {\displaystyle Y} , then its relative price falls. The usual hypothesis is that the quantity demanded of x would increase at the lower price, the law of demand. The generalization to more than two goods consists of modelling y as a composite good.
The second category of passive income is drawing on sources that do not require capital to start, maintain, and grow. These are far better choices for those who want to start out on their own and build a fortune from nothing. They include assets you can create, such as a book, song, patent, trademark, Internet site, recurring commissions, or businesses that earn nearly infinite returns on equity such as a drop-ship e-commerce retailer that has little or no money tied up in operations but still turns a profit.

All wages and any other compensation for services performed in the United States are generally considered to be from sources in the United States. The place, where the personal services are performed, generally determines the source of the personal service income, regardless of where the contract was made, or the place of payment, or the residence of the payer.


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## On Infinite Separations Between Simple and Optimal Mechanisms

### Alexandros Psomas · Ariel Schvartzman Cohenca · S. Weinberg

##### Hall J #825

Keywords: [ correlated distributions ] [ mechanism design ] [ revenue maximization ]

[ Abstract ]
[ [ [
Thu 1 Dec 9 a.m. PST — 11 a.m. PST

Abstract: We consider a revenue-maximizing seller with $k$ heterogeneous items for sale to a single additive buyer, whose values are drawn from a known, possibly correlated prior $\mathcal{D}$. It is known that there exist priors $\mathcal{D}$ such that simple mechanisms --- those with bounded menu complexity --- extract an arbitrarily small fraction of the optimal revenue~(Briest et al. 2015, Hart and Nisan 2019). This paper considers the opposite direction: given a correlated distribution $\mathcal{D}$ witnessing an infinite separation between simple and optimal mechanisms, what can be said about $\mathcal{D}$?\citet{hart2019selling} provides a framework for constructing such $\mathcal{D}$: it takes as input a sequence of $k$-dimensional vectors satisfying some geometric property, and produces a $\mathcal{D}$ witnessing an infinite gap. Our first main result establishes that this framework is without loss: every $\mathcal{D}$ witnessing an infinite separation could have resulted from this framework. An earlier version of their work provided a more streamlined framework (Hart and Nisan 2013). Our second main result establishes that this restrictive framework is not tight. That is, we provide an instance $\mathcal{D}$ witnessing an infinite gap, but which provably could not have resulted from the restrictive framework. As a corollary, we discover a new kind of mechanism which can witness these infinite separations on instances where the previous aligned'' mechanisms do not.

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# I know there are three real roots for cubic however cubic formula is giving me non-real answer. What am I doing wrong?

I want to solve the equation $x^3-x=0$ using this cubic equation. For there to be real roots for the cubic (I know the roots are $x=-1$, $x=0$, $x=1$), I assume there must be a positive inside the inner square root. (Or is that wrong?)

However, when I substitute in $a=1$, $b=0$, $c=-1$, $d=0$, the square root term inside the cube root terms becomes

$$\sqrt{\;\left(\;2(0)^3 - 9(1)(0)(-1) + 27(1)^2(0)\;\right)^2 - 4 \left(\;(0)^2 - 3(1)(-1)\;\right)^3\quad}$$

It gives me $\sqrt{-108}$, which is $10.39i$. Now that I have a non-real number as part of the equation I can't see any way for it to be cancelled or got rid of, even though I know there is a real answer.

Could somebody please tell me how I can get a real answer and what I am doing wrong? Thanks.

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Is there a particular reason as to why you want to use that formula? – Dman Jan 6 at 19:10
I'm trying to find a general formula which I'm using in a more complex question, I just used x^3-x=0 as an example where I couldn't get it to work – Alex Jones Jan 6 at 19:20
Please look at the Wikipedia article on the Casus Irreducibilis. – André Nicolas Jan 6 at 19:31

I didn't check your calculations, but it seems you got into the point which actually made people turn their attention to complex numbers. Complex numbers were not "invented" in order to solve quadractic equations as some people usually tell us, but to solve cubic equations. People discovered a formula for the roots of a cubic polynomial, but then later discovered that in some situations (actually, a lot of them), the equations passed necessarily over complex numbers. Actually, even in situations where all roots are real this happen.

If you do the calculations correctly, the complex numbers will cancel themselves in the end.

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+1. I was going to make the same observation. :) – Blue Jan 6 at 19:13
See Chapter 14: Complex Numbers in Algebra of Stillwell's Mathematics and its History. (Page 275, if the link doesn't take you there directly.) – Blue Jan 6 at 19:41

Okay, so you're getting that operands of the cube root parts of the formula will look like this: $$p + q i \qquad\text{and}\qquad p - q i$$ with some pesky non-zero $q$ (namely, $\sqrt{108}$). Well, these values are conjugates, so that their respective (principal) cube roots are conjugates, as well. For the $x_1$ value in your formula, these conjugate cube roots add together, and their imaginary parts conveniently cancel. The same kind of cancellation happens for the $x_2$ and $x_3$ values, too, because the factors $\frac{1}{2}(1+i\sqrt{3})$ and $\frac{1}{2}(1-i\sqrt{3})$ are themselves conjugates. When the dust settles, you'll have the three real roots you expect.

As @Aloizio points out, this is historically how imaginary numbers snuck into mathematics: as temporary diversions on the way to real solutions of cubic equations. These numbers seemed weird, maybe even scary, but they cancelled in the end so no harm done. Then people started to wonder about a world in which these things didn't always cancel ...

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Thank you! I had assumed that the two parts were the same and that they were both + as opposed to one + and one - – Alex Jones Jan 6 at 19:38