text:
## Friday, July 10, 2020

### The CAFC tackles § 285 in ELECTRONIC COMMUNICATION v. SHOPPERSCHOICE.COM, LLC

As to an award of attorneys fees:

We review a district court’s denial or grant of attorney
fees under § 285 for abuse of discretion. See Highmark Inc.
v. Allcare Health Mgmt. Sys., Inc., 572 U.S. 559, 561 (2014);
1356 (Fed. Cir. 2019) (“We review a district court’s grant of
attorney[] fees under § 285 for abuse of discretion.”). An
abuse of discretion occurs where a district court makes “a
clear error of judgment in weighing relevant factors or in
basing its decision on an error of law or on clearly erroneous factual findings.”
Bayer CropScience AG v. Dow AgroSciences LLC, 851 F.3d 1302, 1306 (Fed. Cir. 2017)
(internal quotation marks and citation omitted). “A factual
finding is clearly erroneous if, despite some supporting evidence,
we are left with the definite and firm conviction
that a mistake has been made.” Insite Vision Inc. v.
Sandoz, Inc., 783 F.3d 853, 858 (Fed. Cir. 2015) (internal
quotation marks and citation omitted). A district court
must “provide a concise but clear explanation of its reasons
for the fee award.” Hensley v. Eckerhart, 461 U.S. 424, 437
(1983); see In re Rembrandt Techs. LP Patent Litig., 899
F.3d 1254, 1276 (Fed. Cir. 2018).

The manner of litigation

The District Court clearly erred by failing to address
ECT’s manner of litigation and the broader context of
ECT’s lawsuit against ShoppersChoice. See generally
J.A. 1626–28. These are relevant considerations. See SFA
Sys., LLC v. Newegg Inc., 793 F.3d 1344, 1350 (Fed.
Cir. 2017) (“[A] pattern of litigation abuses characterized
by the repeated filing of patent infringement actions for the
sole purpose of forcing settlements, with no intention of
testing the merits of one’s claims, is relevant to a district
court’s exceptional case determination under § 285.”). Before the District Court was evidence that ECT sent standardized demand letters and filed repeat patent
infringement actions to obtain low-value “license fees” and
forcing settlements. See Motion for Attorney Fees at 5. For
example, ShoppersChoice provided the District Court with
evidence that, between 2011 and 2015, ECT, under its former name Eclipse, filed lawsuits against at least 150 defendants, alleging infringement of claims in the ’261 patent
and in other patents in the ’261 patent’s family. Id. at 4.
This number does not reflect the additional pre-litigation
demands made by ECT. See generally id. ECT’s demand
for a low-value settlement—ranging from $15,000 to$30,000—and subsequent steps—such as failure to proceed
in litigation past claim construction hearings—indicates
the use of litigation to achieve a quick settlement with no
intention of testing the strength of the patent or its allegations of infringement. See id. at 4–6. Not only did ShoppersChoice provide the District Court with a list of other
court proceedings involving ECT and its demand letters involving claim 11, id. at 5, ShoppersChoice filed the True
Grit opinion with the District Court prior to its attorney fee
determination, J.A. 2155–56.
Indeed, the True Grit opinion reveals problems with
the District Court’s analysis. The opinion provided a detailed account of ECT’s practice of seeking nuisance-value
license fees. True Grit, 2019 WL 3064112, at *8–9. In the
decision, the California District Court concluded that
awarding attorney fees against ECT was appropriate, either “consider[ing] only the litigation history of ECT (as
both ECT and Eclipse IP) or the entire history of the entities that True Grit has demonstrated are related (including
Shipping & Transit[, LLC (‘S&T’)]) the [California District]
Court can discern a clear pattern of serial filings, and also
several (and presumably many more) instances of threats
of litigation, intended only to obtain quick settlements[.]”
Id. at *9. In reviewing ECT’s actions, the California District Court explained that “ECT’s immediate demand for a
low[-]value settlement, apparent willingness to reduce that
amount to avoid any challenge to its patent, and immediate
provision of a [covenant not to sue] to True Grit once the
declaratory judgment action was filed demonstrate ECT’s
‘in terrorem’ tactics—threatening litigation in hopes of a
quick settlement with no intention of ever testing either
the strength of its patent or its allegations of infringement.” Id. Moreover, the California District Court took
judicial notice of “yet another litigious entity,” S&T, “seeking nuisance value patent ‘rents’ that is helmed by many of
the same individuals that control ECT[.]” Id. at *5.

### The CAFC discusses prosecution errors in the Fitbit case; written decision was not "a reasonable resolution"

The outcome of Fitbit v. Valencell:

We hold that Fitbit as a joined party has the right to
appeal the Board’s decisions pertaining to claims 3–5. We
conclude that the Board erred in its rulings concerning
claims 3–5. We vacate the decision that claims 3–5 are not
unpatentable, and remand for determination of the merits
of patentability on the grounds presented in the petition.

Of errors in patents:

The prosecution history shows this conspicuous error, for claims 4 and 5, as filed and throughout the
prosecution, correctly recited their antecedent; and, in a
claim chart filed in preparation for issuance the examiner
was told that there was “no change.” It appears that neither the applicant nor the examiner caught the error. However, the error has come to light, and the Board declined to
accept the parties’ shared view of the correct antecedent.

The preferable agency action is to seek to serve the
agency’s assignment under the America Invents Act, and
to resolve the merits of patentability. Although the Board
does not discuss its authority to correct errors, there is
foundation for such authority in the America Invents Act,
which assured that the Board has authority to amend
claims of issued patents. See 35 U.S.C. § 316(d). And precedent has provided guidelines for district courts to correct
errors in issued patents. See Novo Indus., L.P. v. Micro
Molds Corp., 350 F.3d 1348, 1354 (Fed. Cir. 2003) (“[A] district court can do so if (1) the correction is not subject to
reasonable debate based on consideration of the claim language and the specification and (2) the prosecution history
does not suggest a different interpretation of the claims.”);
F.3d 1353, 1358 (Fed. Cir. 2011) (the district court can correct an obvious drafting error). The concept of error correction is not new to the Agency, which is authorized to issue
Certificates of Correction.

(...)

Although the Board states that
the intended meaning of the claims is “subject to reasonable debate,” we perceive no debate. Rather, the parties to
this proceeding agree as to the error and its correction. The
Board erred in declining to accept the parties’ uniform position and correct the error that claim 4 depend from
claim 3. With this correction, the rejection of claims 4 and
5 for absence of antecedent basis for “the application” disappears.
We conclude that the Agency’s treatment of this error
as the basis of a Final Written Decision of patentability is
not a reasonable resolution, and does not comport with the
Agency’s assignment to resolve patentability issues. On
the correct antecedent basis, the petition’s issue of obviousness may be resolved by the Board, in furtherance of resolution of the parties’ dispute in concurrent district court
litigation.
The Board’s Final Written Decision on the ground of
“absence of antecedent” basis is vacated. On remand the
Board shall determine patentability of corrected claims 4
and 5 on the asserted grounds of obviousness.

### CAFC interprets Hatch-Waxman in Genentech v. Immunex

Genentech filed two motions in the District of Delaware seeking to preclude Amgen from commercially marketing Mvasi “until such time as Amgen . . . provides notice
of its intent to commercially market such product[] pursuant to [42] U.S.C. § 262(l)(8) and 180 days have elapsed.”
J.A. 3. It argued that Amgen’s third and fourth supplements resulted in new and distinct applications that require new notices under Section 262(l)(8)(A). The district
court denied both motions, reasoning that Amgen’s October
2017 commercial marketing notice for Mvasi satisfied Section 262(l)(8)(A)’s notice requirements. Genentech appeals. We have jurisdiction under 28 U.S.C. §§ 1292(a)(1)
and (c)(1).

(...)

Our interpretation is consistent with the Supreme
Court’s decision in Sandoz Inc. v. Amgen Inc., 137 S. Ct.
1664 (2017) (Sandoz II). In Sandoz II, the Supreme Court
explained that the term “licensed” in Section 262(l)(8)(A)
simply means that the product must be licensed on the date
of the first commercial marketing, id. at 1677, not that each
supplemental application results in a new license requiring
the biosimilar applicant provide further notice. In fact,
Sandoz II recognized that “nothing in § 262(l)(8)(A) turns
on the precise status or characteristics of the biosimilar application.” Id. at 1678. Section 262(l)(8)(A)’s notice requirement is separate from Section 262(k)’s licensure
requirements. Sandoz II also explained that “Section
262(l)(8)(A) contains a single timing requirement: The applicant must provide notice at least 180 days prior to marketing its biosimilar.” Id. at 1677. Thus, Genentech’s
interpretation, which would impose several timing requirements where each supplement necessarily triggers another
notice requirement, is inconsistent with the statute and
with Sandoz II. A biosimilar applicant that has already
provided Section 262(l)(8)(A) notice regarding its biological
product need not provide another notice for each supplemental application concerning the same biological product.
Accordingly, we conclude that Amgen’s October 6,
2017, letter, which notified Genentech of Amgen’s intent to
commercially market Mvasi at least 180 days before its
July 2019 launch, satisfied Section 262(l)(8)(A).

### The CAFC tackles "filing under seal" in Uniloc v Apple

The issue of sealing records from public view:

In its sealing motions, Uniloc asked the district court
to seal most of the materials in the parties’ underlying
briefs, including citations to case law and quotations from
published opinions. J.A. 414–15; see J.A. 279–87. It also
requested that the court seal twenty-three exhibits in their
entireties. J.A. 414–15; see J.A. 299–412, 422, 503. These
exhibits included matters of public record, such as a list of
Uniloc’s active patent cases. See J.A. 388.

In support of its sealing requests, Uniloc filed three
short declarations. See J.A. 413–16, 420–22, 502–04.
These declarations listed the exhibits Uniloc sought to seal
and stated that these exhibits “contain[ed] sensitive, confidential and
proprietary information related to financial
data, licensing terms and business plans with respect to
various Uniloc entities” and that “disclosure of this extremely sensitive
information would create a substantial
risk of serious harm to the Uniloc entities.” J.A. 503; see
also J.A. 414–15, 422.

(...)

On November 28, 2018, the Electronic Frontier Foundation (“EFF”)
contacted counsel for Uniloc, asserting that
its proposed redactions were excessive. J.A. 768.3 EFF
stated, moreover, that if the documents at issue were not
“re-filed consistent with the public’s right of access,” it
would move to formally intervene in the case and “ask the
court to . . . unseal improperly withheld material.” J.A.
768. After Uniloc declined to revise its sealing requests,
EFF filed a motion to intervene for the purpose of opposing
Uniloc’s sealing motions. J.A. 53.
On January 17, 2019, the district court denied, in full,
failed to provide “a compelling reason to justify sealing.”4
Sealing Order, slip op. at 1. According to the court, Uniloc’s
“generalized assertion of potential competitive harm
fail[ed] to outweigh the public’s right to learn of the ownership
of the patents-in-suit—which grant said owner the
right to publicly exclude others.” Id. at 2.
The court stated, moreover, that Uniloc’s request to
seal covered an “astonishing” amount of material. Id. In
support, it noted that Uniloc sought “to seal the majority of
exhibits and large swaths of briefing and declarations,” including
portions of Apple’s motion to dismiss “that simply
quote[d] Federal Circuit law.” Id.

The collateral order doctrine

As a general rule, the jurisdictional reach of the
federal appellate courts extends only to “final decisions of
the district courts of the United States.” 28 U.S.C. § 1291.
The collateral order doctrine, however, provides a “narrow
exception” to the final judgment rule, permitting appellate
review of “trial court orders affecting rights that will be
irretrievably lost in the absence of an immediate appeal.”
Richardson-Merrell, Inc. v. Koller, 472 U.S. 424, 430–31
(1985) (citation and internal quotation marks omitted); see
also Cohen v. Beneficial Indus. Loan Corp., 337 U.S. 541,
546 (1949) (explaining that there is a right to appeal a
“small class” of orders “which finally determine claims of
right separable from, and collateral to, rights asserted in
the action, too important to be denied review and too independent of the
cause itself to require that appellate consideration be deferred until the whole case is adjudicated”).
To fall within the collateral order doctrine, “an order
must at a minimum satisfy three conditions: It must [1]
‘conclusively determine the disputed question,’ [2] ‘resolve
an important issue completely separate from the merits of
the action,’ and [3] ‘be effectively unreviewable on appeal
from a final judgment.’” Richardson-Merrell, 472 U.S. at
431 (quoting Coopers & Lybrand v. Livesay, 437 U.S. 463,
468 (1978)); see Apple I, 727 F.3d at 1220. These requirements are met here.

“It is clear that the courts of this country recognize a
general right to inspect and copy public records and documents, including judicial records and documents.” Nixon
v. Warner Commc’ns, Inc., 435 U.S. 589, 597 (1978) (footnotes omitted); see Ex parte Uppercu, 239 U.S. 435, 439–41
(1915). This right of access supports “the citizen’s desire to
keep a watchful eye on the workings of public agencies.”
Nixon, 435 U.S. at 598; see also Metlife, Inc. v. Fin. Stability
Oversight Council, 865 F.3d 661, 665 (D.C. Cir. 2017)
(“Like the First Amendment . . . the right of inspection
serves to produce an informed and enlightened public opinion.” (citation and internal quotation marks omitted)).
There is a strong presumption in favor of access to documents filed with a court. See Ctr. for Auto Safety, 809
F.3d at 1096; see also In re Violation of Rule 28(D), 635 F.3d
1352, 1356 (Fed. Cir. 2011). “The presumption of access is
‘based on the need for federal courts, although independent—indeed, particularly because they are independent—
to have a measure of accountability and for the public to
have confidence in the administration of justice.’” Ctr. for
Auto Safety, 809 F.3d at 1096 (quoting United States v.
Broad. Co. v. U.S. Dist. Ct. for the Dist. Nev., 798 F.2d 1289,
1294 (9th Cir. 1986) (emphasizing that the presumption of
public access “promot[es] the public’s understanding of the
judicial process and of significant public events”).

As to reconsideration

We do not find this argument persuasive. Under Local
Rule 7-9, a litigant, in order to obtain leave to file a motion
for reconsideration, must establish:
(1) That at the time of the motion for leave, a material difference in fact or law exists from that
which was presented to the Court before entry of
the interlocutory order for which reconsideration is
sought. The party also must show that in the exercise of reasonable diligence the party applying for
reconsideration did not know such fact or law at the
time of the interlocutory order; or
(2) The emergence of new material facts or a
change of law occurring after the time of such order; or
(3) A manifest failure by the Court to consider material facts or dispositive legal arguments which
were presented to the Court before such interlocutory order.
N.D. Cal. Civ. Local R. 7-9(b).

A backwards argument

Uniloc further maintains that the district court erred
in refusing to redact the specific dollar amounts and financial terms in certain agreements because Apple’s motion to
dismiss for lack of subject matter jurisdiction “‘did not directly depend’” on this information. Br. of Appellants 26
(quoting Reconsideration Order, 2019 WL 2009318, at *2).
In support, it argues that although Apple alleged that
“Uniloc was . . . required to license its patents for at least a
certain amount of money by a certain deadline,” it was irrelevant “whether the threshold was $10,000,000 or$10.”
Id.
This argument has it backwards. See Kamakana, 447
F.3d at 1181–82. The district court was not required to seal
any information that was not “directly relevant” to its ruling on Apple’s motion to dismiss; instead, all filings were
presumptively accessible, and it was Uniloc’s duty to provide compelling reasons for shielding particular materials
from public view. See, e.g., Ctr. for Auto Safety, 809 F.3d
at 1098 (“[O]ur precedent . . . presumes that the compelling
reasons standard applies to most judicial records.” (citations and internal quotation marks omitted)); Kamakana,
447 F.3d at 1182 (“The judge need not document compelling reasons to unseal; rather the proponent of sealing
bears the burden with respect to sealing.”).

Note

Trial court judges, heavily burdened with the task of
resolving complex legal and factual disputes, must also
serve as the gatekeepers for vast quantities of information.
They should not be forced to spend large swaths of their
time struggling to rein in overzealous efforts to seal. See
Reconsideration Order, 2019 WL 2009318, at *2 n.2 (“Because of the frequently overbroad requests to seal arising
in patent litigation today, the Court . . . must now deal with
these burdensome motions to seal on a regular basis.”); see
also Takeda Pharm. U.S.A., Inc. v. Mylan Pharm., Inc., No.
cv-19-2216-RGA, 2019 WL 6910264, at *1 (D. Del. Dec. 19,
2019) (“In my experience, corporate parties in complex litigation generally prefer to litigate in secret. To that end,
discovery is over-designated as being confidential, pleadings and briefs are filed under seal, redacted versions of
sealed documents are over-redacted, requests are made to
seal portions of transcripts of judicial proceedings, and parties want to close the courtroom during testimony.”); Cardiac Pacemakers, Inc. v. St. Jude Med., Inc., No. 1:96-cv1718-DFH-TAB, 2007 WL 141923, at *2 (S.D. Ind. Jan. 16,
2007) (“[A]ll too frequently this Court finds itself reviewing
overbroad and unsupported requests to file documents under seal. Lest practitioners suspect the Court is overstating its case, counsel in one case recently filed a motion
seeking to file excerpts from the Federal Register under
seal.”).

### What is the truth about Covid testing in New Jersey in July 2020?

From a post on nj.com on July 10, 2020:

Officials have said the transmission rate and positivity rate are the two most important figures to measure how the virus is currently spreading across the state, helping determine when restrictions can be lifted.

“And feeding into both of these metrics are the results of the coronavirus tests being recorded every day,” Gov. Phil Murphy said at his latest coronavirus briefing in Trenton. “The more testing, the more precise we can get these numbers.”

In fact, the two major testing sites in New Jersey closed on June 30, 2020:

The drive-through coronavirus testing sites at Bergen Community College in Paramus and the PNC Bank Arts Center in Holmdel will close June 30 as federal support ends.

But the Federal Emergency Management Agency and the U.S. Department of Health and Human Services will continue to support ongoing testing at local pharmacies through at least the end of August.

As to locales for testing in Somerset County, New Jersey, one had the RVCC site, once serving residents of Hunterdon and Somerset Counties, but now only for Somerset County residents. Initially, the RVCC site would NOT test asymptomatic individuals:

Raritan Valley Community College, 118 Lamington Road. COVID-19 drive-thru testing site. Residents can make an appointment by visiting here or call (908) 237-7150. Testing will be by appointment only and a valid doctor’s prescription is required. Initially, the test site at RVCC will be open from 10 a.m. to 1 p.m. on certain dates. Check here for updates. Testing is free and only available to Hunterdon and Somerset County residents, age 5 and older, with symptoms, such as fever, dry cough and shortness of breath. Must have a written doctor’s authorization and show proof of residency, such as a valid driver’s license or state-issued identification.

This restriction was lifted, BUT the RVCC site has stopped taking appointments. Thus, on Wednesday, July 8, 2020, an internet submission did get an acknowledgement:

**

Date: Wed, Jul 8, 2020 10:18 AM
To: ZZZZ;
Cc:

Hi YYYY,

Thank you for your submission. We are working quickly to schedule your appointment. Soon you will receive a text and email with your appointment information.

**

An inquiry on July 9 produced no response

**

Just to confirm, I have received no scheduled appointment.

Sent July 9 at 1:20pm

**

No response has been given as of July 10.

Contacting the CVS site on Union Ave., as an asymptomatic 70 year old gives the following:

Thus, while Governor Murphy speaks about the value of testing, New Jersey is in fact a "testing-unfriendly" state.

We will talk about how the decisions on testing in New Jersey impact the accuracy, and significance, of the transmission rate and positivity rate in a separate post.

## Thursday, June 25, 2020

### Covid testing in New Jersey: a tale of two websites

Is New Jersey testing asymptomatic people?

**one internet site says

Testing is available to everyone in New Jersey. Anyone who wants a COVID-19 diagnostic test, can now get one at any of the 250+ testing sites across New Jersey.

To help meet this demand, Attorney General Gurbir Grewal along with the Division of Consumer Affairs, has authorized the more than 18,000 licensed pharmacists in New Jersey to administer FDA-approved or authorized COVID-19 tests to their customers.

Moreover, the Division's order allows for these tests to be given without a prescription, and removes the requirement that pharmacists enter into explicit collaborative practice agreements with a physician.

**
But the Somerset/Hunterdon NJ site at RVCC tells a different story as of Thursday, June 25, Friday June 26, 2020:

New Date Added for COVID-19 Drive-thru Testing
July 2, 2020
Post Date:06/19/2020 2:32 PM

BRANCHBURG – Somerset County is announcing an additional date of Thursday, July 2, for COVID-19 drive-thru testing at Raritan Valley Community College [RVCC]. Reservations for June 25 have been filled, but spaces are currently available on the first Thursday in July.

Testing, which is free of charge, is open to Hunterdon and Somerset County residents, age five (5) and older, who are exhibiting symptoms. Residents must have a valid doctor’s prescription, ID and an appointment to receive testing.

Appointments for July 2 can be scheduled online at https://somerset-hunterdon.adlabscovidtest.com. Residents who do not have computer access or who would like to schedule an appointment for children age five to 18 years old can call the COVID-19 testing information line at 908-237-7150, Monday through Friday, from 9 a.m. to 1 p.m.

Patients are required to provide a copy of their prescription, either by bringing it with them to the testing site, or by sending a copy in advance. Prescriptions can be sent via email to coronavirus@co.somerset.nj.us, with the word “Prescription” in the subject line, or faxed to 908-704-8042.

For the safety, health and security of staff and volunteers, patients must arrive by car. The testing site will not allow entry if residents don’t arrive in a vehicle, even if they have a valid driver’s license and prescription. When coming to the testing center, residents are asked to use the main entrance to the college campus, off of Route 28.

Anyone who does not have an appointment and a valid prescription or written order from their physician will be turned away.

## Sunday, June 21, 2020

### Chuck Todd flunks history 101

On Sunday, 21 June 2020, 0n Meet the Press, Chuck Todd said of Juneteenth:

Alright, let me pause it here. When we come back, there were events across the country this weekend marking Juneteenth, which celebrates the end of slavery in the United States. Up next, why those celebrations may be even bigger next year, and beyond.

[CHUCK TODD resumes:]

Welcome back. Data download time. For many Americans, June 19th, Juneteenth, has long held a special meaning. But for others, especially many white Americans, this was the year it was suddenly recognized everywhere. Even so, momentum to recognize the holiday has actually been building for quite some time. First, let's talk about what it is. Juneteenth commemorates June 19th, 1865. It is the day that Union troops arrived in Galveston, Texas to announce the Civil War was over. The news hadn't reached Galveston yet. And to inform people that the Emancipation Proclamation had freed all enslaved people nationwide. It was more than 100 years later that Texas made Juneteenth an official holiday. And since then, 46 other states and the District of Columbia have joined Texas and done the same, with most doing so since the year 2000.

On 19 June 1865, Major General Gordon Granger announced the Emancipation Proclamation at Galveston, Texas, formally declaring the end of slavery in Texas. Slavery in the United States, especially as to Kentucky and Delaware, would not end until December 1865, with the adoption of the 13th Amendment.

Earlier, on May 13, 1865, the last land battle of the war was fought at Palmito Ranch, near Brownsville, Texas. Some of the Union troops were African Americans, who were well aware of the Emancipation Proclamation and of the surrender of General Lee.

On June 2, 1865, General Edmund Kirby Smith surrendered the Department of the Trans-Mississippi to Major General Edward Canby at Galveston, Texas. The citizens of Galveston were well aware of the status of the war more than two weeks before Granger's proclamation.

It was not until August 20, 1866, more than one year AFTER June 19, 1865, that President Andrew Johnson declared the insurrection officially over and peace restored.

Chuck Todd's "data download" is not only erroneous (slavery in the United States did not end until December 1865 and the Civil War was not deemed over in June 1865) and missing in key details (people in Texas generally and Galveston in particular knew of the status of the war, and of the Emancipation Proclamation before June 19, 1865).

Kirby Smith, who would be the last living full General of the Confederacy (Lee was only number 3 in rank) apparently believed Lee and Johnston had been imprisoned, and would exit to Mexico to avoid being tried for treason.

### Governor Cuomo on CBS Sunday Morning on June 21, 2020

Back on June 13, Governor Cuomo of New York quoted numbers created by Instagram people defining an Rt parameter to state that New York had done the best job in the nation controlling Covid19. New Jersey was second best. Hawaii weighed in at 0.99.

In the interview which aired on June 21 on CBS Sunday Morning, Governor Cuomo obliquely referred to the same Instagram numbers. However, on June 21, ten states had lower values of Rt than that of New York. Hawaii, which was below 1.0 on June 13, became the worst state in the nation at an Rt of 1.47, topping that of the second worst state, Florida, which had 1.35.

The website for the Rt numbers is https://rt.live/ , and notes:

While we make a best effort to accurately describe Rt, nothing can do that perfectly. Please calibrate with other sources, like epiforecasts.io, as well.

If the Rt parameter is truly "predictive," one wonders why there are such dramatic swings.

link to CBS interview, at 9:44 minutes, the longest segment on CBS Sunday Morning on June 21, 2020:
https://www.cbs.com/shows/cbs-sunday-morning/video/_nyBbUlBviFb1uBi4Q_ObIcXwDqjKjMR/in-conversation-with-andrew-cuomo/

The moment of nature on CBS Sunday Morning on June 21 was great horned owls at Lake Erie.

## Monday, June 15, 2020

### With a low Rt, will New York quarantine out-of-staters entering New York??

After New York Governor Cuomo's briefing on June 12, 2020, which included text

Rate of Transmission [Rt[ of .77 Lowest Out of All 50 States

(...)

So we are the exact opposite. We, since we've reopened, the number has continued to go down, believe it or not. We reopened. It continues to go down because we've been disciplined in our reopening, and that's what we have to continue to do. This is a website where the founders of Instagram now track the rate of transmission of states across the nation. New York State, the lowest rate of transmission, meaning the virus is spreading at the lowest rate in the State of New York, of every state in America, that is incredible. We were the number one state in terms of infection, number one in the nation, number one on the globe per capita, and now we're the last state in terms of rate of transmission. That is because New Yorkers stepped up, they were smart, they were disciplined, they did what they had to do, and we have to stay there. We have to stay there. Now is no time to forget what got us here. We have to stay smart.

***

***
I joked to a friend that the next thing that would happen would be an attempt by New York to quarantine out of state people coming INTO New York.

Well, one only had to wait till Monday, June 15. The CBS880 link paraphrases Cuomo's remark as

The governor says a primary concern right now is contagion coming from outsiders who are visiting New York.

The actual audio is a bit more interesting.

****Separately, some background on Ro

From wikipedia:

During an epidemic, typically the number of diagnosed infections N(t) over time t is known. In the early stages of an epidemic, growth is exponential, with a logarithmic growth rate[citation needed]

{\displaystyle K={\frac {d\ln(N)}{dt}}.}
For exponential growth, N can be interpreted as the cumulative number of diagnoses (including individuals who have recovered) or the present number of diagnosed patients; the logarithmic growth rate is the same for either definition. In order to estimate R_{0}, assumptions are necessary about the time delay between infection and diagnosis and the time between infection and starting to be infectious.

In exponential growth, K is related to the doubling time T_{d} as

{\displaystyle K={\frac {\ln(2)}{T_{d}}}}.
Simple model
If an individual, after getting infected, infects exactly R_{0} new individuals only after exactly a time \tau (the serial interval) has passed, then the number of infectious individuals over time grows as

{\displaystyle n_{E}(t)=n_{E}(0)\,R_{0}^{t/\tau }}
or

{\displaystyle log(n_{E}(t))=log(n_{E}(0))+log(R_{0})t/\tau .}
In this case,

{\displaystyle R_{0}=e^{K\tau }} or {\displaystyle K={\frac {\ln R_{0}}{\tau }}}.
For example, with {\displaystyle \tau =5~\mathrm {d} } and {\displaystyle K=0.183~\mathrm {d} ^{-1}}, we would find {\displaystyle R_{0}=2.5}.

Definitions from article by Y. Ma (2018) [
Epidemiol Infect. 2018 Sep; 146(12): 1478–1494.
Published online 2018 Jul 4. doi: 10.1017/S0950268818001760
]

The reproductive number and serial interval (SI) are two key quantities in describing transmission of an infectious disease. The reproductive number is defined as the average number of secondary cases a primary infectious case will produce. In a totally susceptible population, it is referred to as the basic reproductive number (R0); it is referred to as the effective reproductive number (Re) if the population includes both susceptible and non-susceptible persons [6]. An Re greater than 1 indicates that the disease will continue to spread while an Re less than 1 indicates that the disease will eventually die out. Although the reproductive number is usually defined as the average number of secondary cases, it is occasionally defined as the average number of secondary infections [7–10], a distinction that is important for a disease with a long incubation period (the time between infection and developing symptomatic disease) and/or only a fraction of infections progressing to disease. Depending on the setting, the reproductive number can be expressed as a function of parameters such as infection rate, contact rate, recovery rate, making it useful in determining whether or not a disease can spread through a population.

The serial interval (SI), defined as the time between disease symptom onset of a case and that of its infector [11], is a surrogate for the generation interval— an unobservable quantity defined as the time between the infection of a case and the time of infection of its infector [12]. The SI is an important quantity in the interpretation of infectious disease surveillance data, in the identification of outbreaks, and in the optimization of quarantine and contact tracing.

[lbe note: the serial interval is the time between when the infector shows symptoms and the infectee shows symptoms. If asymptomatic people can infect others, one immediately sees a problem here. R becomes undefined if tau becomes undefined.]

***As to covid19, one would have to estimate serial interval from information OUTSIDE OF new cases/per day, but this could be done and such number would be expected to be a known number with a range of uncertainty.
However, R is not knowable from new cases per day or from any data available. In fact, in the tb case, one creates models and chooses R based on a "best fit." From Ma on tb:

Three articles used either approximate Bayesian or exact likelihood methods, 24 articles used either a mathematical model fit with empirical data or a descriptive/regression approach on empirical data, and 29 articles used a simulation based mathematical model

### Parameters involved in Covid19 forecasts

**New York Governor Cuomo said:

So we are the exact opposite. We, since we've reopened, the number has continued to go down, believe it or not. We reopened. It continues to go down because we've been disciplined in our reopening, and that's what we have to continue to do. This is a website where the founders of Instagram now track the rate of transmission of states across the nation. New York State, the lowest rate of transmission, meaning the virus is spreading at the lowest rate in the State of New York, of every state in America, that is incredible.

**

From rt.live:

These are up-to-date values for Rt, a key measure of how fast the virus is growing. It’s the average number of people who become infected by an infectious person. If Rt is above 1.0, the virus will spread quickly. When Rt is below 1.0, the virus will stop spreading.

The metric being tracked here (Rt) represents the effective reproduction rate of the virus calculated for each locale. It lets us estimate how many secondary infections are likely to occur from a single infection in a specific area. Values over 1.0 mean we should expect more cases in that area, values under 1.0 mean we should expect fewer

The new version of this model accounts for variation in serial interval and delay between onset of symptoms and a positive test. Because of these changes, it is also more robust to large changes in reported tests. However, this also means that Rt will be far less variable day-to-day than the previous model. [This sounds like Ro.]

There is an incubation period in which people are likely infectious but not symptomatic. This model assumes infectiousness begins with symptoms. While future versions may correct for this, a simple heuristic is to shift all values of Rt 5 days into the past.
While we make a best effort to accurately describe Rt, nothing can do that perfectly.

**

One cannot be sure "how qualified" the people at Instagram are to assess Rt, which does sound like Ro. Their Rt is clearly NOT a rate; it is dimensionless. If you believe this stuff, you should be worried, because Hawaii is at 0.99, not like a safe state like NY or NJ, which are the two "best" states (lowest Rt)

As usual, the data relied upon is tests of symptomatic people. Although they make a nod to pre-symptomatic people, they ignore asymptomatic people (who never get symptoms). If one is worried about the kinetics of spreading, this is incomplete, because it ignores: asymptomatic to symptomatic, symptomatic to asymptomatic and asymptomatic to asymptomatic.

At this point in time, this is not a viable approach.

Recent work by Aravinda de Silva of UNC shows how we can fine tune analysis of "asymptomatic" individuals.

From Genetic and Engineering News:

The antibody test is based on the receptor-binding domain (RBD) of the spike protein. The RBD-based antibody test measures the levels of that domain, which the authors found correlate to the levels of neutralizing antibodies related to the paper published in Science Immunology titled “The receptor-binding domain of the viral spike protein is an immunodominant and highly specific target of antibodies in SARS-CoV-2 patients.”

[The importance resides in specificity to Covid19]

The RBD of the spike protein in SARS-CoV-2 is not shared among other known human or animal coronaviruses. Therefore, antibodies against this domain are likely to be highly specific to SARS-CoV-2, and so these antibodies reveal if an individual has been exposed to the virus that can cause COVID-19.

[Of data]

By day 9 after the onset of symptoms, the authors wrote that “the recombinant SARS-CoV-2 RBD antigen was highly sensitive (98%) and specific (100%) for antibodies induced by SARS-CoVs.” They noted that they observed a strong correlation “between levels of RBD binding antibodies and SARS-CoV-2 neutralizing antibodies in patients.”

[Of the relevance to asymptomatic people]

“We don’t see our research as a means to replace commercial tests,” said de Silva. “Commercial tests are critical, especially for making decisions about the clinical management of individual patients. But it’s too early in the pandemic to know if the commercial assays are suitable for identifying people who experienced very mild or no disease after infection or if the assays tell us anything about protective immunity, as researchers are still learning about this virus.”

### Did Jefferson Davis commit treason?

The Guardian discussed Jefferson Davis on 13 June 2020:

The Confederacy lost the war and slavery was abolished under the 13th amendment, ratified in December 1865. Davis was charged with treason but never tried, having his citizenship stripped instead. He died in New Orleans in 1889.

Jefferson Davis was indicted by a grand jury convened by federal district court judge John Underwood. From there, the story gets complicated, related in part to presidential ambitions of Salmon Chase (then Chief Justice of the Supreme Court) and the overlapping-in-time impeachment of Andrew Johnson.

At the time of the indictment, federal high crimes (such as treason) had to be overseen by the district judge in the jurisdiction of the crime (here Virginia, the location of Judge Underwood) and the relevant Supreme Court Justice (here, Salmon Chase, who oversaw the Fourth Circuit). Chase could foretell that the case would involve the legality of secession. Jefferson Davis would argue Davis did not commit treason, because he was no longer a citizen of the United States. If secession were constitutional, this might be a valid defense. Chase himself had states rights leanings, even though he was an abolitionist. Of all people, Thaddeus Stevens offered to defend Davis, because Stevens wanted the Confederacy to be viewed as a conquered nation, under complete military control.

The impeachment proceedings against Johnson kept delaying Davis' trial. Horace Greeley and Cornelius Vanderbilt helped to obtain bail for Davis.
Chase ruled that section 3 of the 14th Amendment, which gave limitations of rights on former Confederate officials, defined the ONLY limitations which could be imposed. Thus, effectively, the indictment for treason was unconstitutional. Johnson pardoned Davis before the full Supreme Court could rule on treason by Davis.

Ironically, both Chase and Johnson were considering running as Democrats in the 1872 election. Johnson, after all, was a Democrat, and Chase was shifting.

https://www.scotusblog.com/2017/10/chief-justice-salmon-chase-permanency-union-cynthia-nicoletti-chases-political-ambitions/

Washington Post, In 1868, the fate of Jefferson Davis’s neck swung on Andrew Johnson’s impeachment, Ronald G. Shafer
Feb. 2, 2020 at 7:00 a.m. EST

**Some have argued that the federal government, in referring to its naval action against the Confederacy as a blockade (as distinct from a port closing) admitted that the Confederacy was a sovereign government

## Sunday, June 14, 2020

### On the meaning of "Juneteenth"

One commenter on the Trump/Juneteenth/Carson matter wrote the following:

Carson...was "pleasantly surprised" by how much Trump knew about Juneteenth, which commemorates the end of slavery in the United States."

He was surprised Trump knew anything at all. Note how Carson didn't detail what Trump knew about it.

June 19 became "Juneteenth" because on June 19, 1865, Union major general Gordon Granger informed residents of Galveston, Texas that slaves in Texas were free by virtue of the Emancipation Proclamation, which had taken effect, in Texas, on January 1, 1863. The state of Texas, one of eleven states of the Confederacy, was the last Confederate state to fall, at least nominally, under control of Union forces, and thus ended slavery in the Confederate states, although not exactly by virtue of the Emancipation Proclamation.

The above commenter is wrong because Juneteenth does not mark the end of slavery in the United States.

Henry Louis Gates, Jr. wrote

The Emancipation Proclamation itself, ending slavery in the Confederacy (at least on paper), had taken effect two-and-a-half years before [Juneteenth], and in the interim, close to 200,000 black men had enlisted

But even this is not correct. The Emancipation Proclamation mentions only ten of the eleven Confederate states, pointedly omitting the state of Tennessee. The Emancipation Proclamation did not end slavery in Tennessee. Separately, the Emancipation Proclamation also excluded certain parts of Louisiana and Virginia. Further, the Emancipation Proclamation did not end slavery in the border (slave) states of Missouri, Kentucky Maryland, and Delaware. [There was alavery in New Jersey, but that is a different story.]

By the time of Juneteenth 1865, slavery had been eliminated by state action in Missouri, Maryland, and Tennessee.

However, this technicality does not absolve the commentator (or others who believe the Juneteenth celebrates the end of slavery) because slavery did not end in Kentucky and Delaware until the adoption of the Thirteenth Amendment on December 18, 1865.

In fact, Delaware did not ratify the the 13th Amendment until 1901; Kentucky until 1976. Of interest, one notes both Civil War presidents, Lincoln and Davis, came from Kentucky.

In passing, one notes that the following map from ushistory.org

is in error:

## Friday, May 22, 2020

### CAFC affirms ED Va in Odyssey case

This case presents three Administrative Procedure Act
challenges involving the United States Patent and Trademark Office. Odyssey challenges procedural actions taken
by the PTO in two patent applications and makes a third
facial challenge to certain PTO procedural rules governing
practice before the Patent Trial and Appeal Board in ex
parte appeals. The Eastern District of Virginia dismissed
the former two challenges for lack of subject matter jurisdiction because the PTO had not taken final agency action.
It dismissed the latter challenge as barred by 28 U.S.C.
§ 2401, the six-year statute of limitations for challenges to
agency action. Because we agree with the district court
that the first two challenges concern non-final agency action and the latter challenge is barred by § 2401, we affirm.

## Wednesday, May 20, 2020

### Bandai wins on non-infringement but not invalidity at the CAFC

Of the indefinite articles a or an:

McRO offers two arguments that this specification evidence should be interpreted differently. The first argument, which relies on the key definitional sentence,
misreads our precedent and ignores most of the language
in that sentence. According to McRO, the phrase “a vector
from each vertex n on the reference” implies that each vertex on the reference can have multiple corresponding vectors because “it is a well settled rule that the article ‘a’
means one or more and not ‘a single.’” Brief for Appellant
at 24 (citing KCJ Corp. v. Kinetic Concepts, Inc., 223 F.3d
1351, 1356 (Fed. Cir. 2000)). The patent would have used
the phrase “a single vector,” McRO argues, if it had meant
to require one-to-one correspondence. Id. But McRO misreads KCJ Corp., which explains that “an indefinite article
‘a’ or ‘an’ in patent parlance carries the meaning of ‘one or
more’ in open-ended claims containing the transitional
phrase ‘comprising.’” 223 F.3d at 1356 (emphasis added).
This specific canon of claim construction has no bearing
here. And as discussed, the word “a” is hardly the only relevant textual evidence of meaning.

As to invalidity, the district court's reasoning was conclusory:

McRO offers two arguments that this specification evidence should be interpreted differently. The first argument, which relies on the key definitional sentence,
misreads our precedent and ignores most of the language
in that sentence. According to McRO, the phrase “a vector
from each vertex n on the reference” implies that each vertex on the reference can have multiple corresponding vectors because “it is a well settled rule that the article ‘a’
means one or more and not ‘a single.’” Brief for Appellant
at 24 (citing KCJ Corp. v. Kinetic Concepts, Inc., 223 F.3d
1351, 1356 (Fed. Cir. 2000)). The patent would have used
the phrase “a single vector,” McRO argues, if it had meant
to require one-to-one correspondence. Id. But McRO misreads KCJ Corp., which explains that “an indefinite article
‘a’ or ‘an’ in patent parlance carries the meaning of ‘one or
more’ in open-ended claims containing the transitional
phrase ‘comprising.’” 223 F.3d at 1356 (emphasis added).
This specific canon of claim construction has no bearing
here. And as discussed, the word “a” is hardly the only relevant textual evidence of meaning.

Juicy Whip vs. Orange Bang appears in footnote 4:

We deny McRO’s request to direct that the case be
assigned to a different district judge on remand. See Juicy
Whip, Inc. v. Orange Bang, Inc., 382 F.3d 1367, 1371, 1373–
74 (Fed. Cir. 2004).


text:
# Principal Components Analysis (PCA)

In this section, we’re going to go over a few introductory techniques for visualizing and exploring a single cell dataset. This is an essential analysis step, and will tell us a lot about the nature of the data we’re working with. We’ll figure out things like:

• If the data exists on a trajectory, clusters, or a mix of both
• How many kinds of cells are likely present in a dataset
• If there are batch effects between samples
• If there are technical artifacts remaining after preprocessing

We’re going to use two main tools for this analysis: PCA and PHATE. PCA is useful because it’s quick and serves as a preliminary readout of what’s going on in a sample. However, PCA has many limitations as a visualization method because it can only recover linear combinations of genes. To get a better sense of the underlying structure of our dataset, we’ll use PHATE.

## 2.0 - What is a visualization?

Before we get too deep into showing a bunch of plots, I want to spend a little time discussing visualizations. Skip ahead if you want, but I think it’s important to understand what a visualization is, and what you can or cannot get from it.

#### A visualization is a reduction of dimensions

When we talk about data, we often consider the number of observations and the number of dimensions. In single cell RNA-seq, the number of observations is the number of cells in a dataset. In other words, this is the number of rows. The number of dimensions, or number of features, is the number of genes. These are the columns in a gene expression matrix.

In a common experiment you might have 15,000-30,000 genes in a dataset measured across 5,000-100,000 cells. This presents a problem: How do you visually inspect such a dataset? The key is to figure out a way how to draw the relationships between points on a 2-dimensional sheet of paper, or if you add linear perspective, you can squeeze in a third dimension.

A visualization is simply figuring out how to go from 30,000 dimensions -> 2-3.

#### Heatmaps allow you to look at all genes across all cells simultaneously

One way is to look at a heatmap. Here I’ve created a clustered heatmap from the Datlinger data using seaborn.clustermap:

import seaborn as sns
cg = sns.clustermap(t_cell_data, cmap='inferno', xticklabels=[], yticklabels=[])
cg.ax_heatmap.set_xlabel('Genes ({})'.format(t_cell_data.shape[1]))
cg.ax_heatmap.set_ylabel('Cells ({})'.format(t_cell_data.shape[0]))

It’s hard to draw any conclusions from this. How close together are any two cells? How do genes covary? We get some sense of this, and we are getting to look at all genes across all cells, but this representation of the data hinders hypothesis generation.

#### Biplots show gene-gene relationships

Another natural presentation is the biplot, commonly used for FACS analysis. Here each axis represents the expression of one of two genes and each dot is a cell. Let’s look at a biplot for some genes from the Datlinger dataset.

As you can see, it’s much easier to identify gene-gene relationships, but you can see how complex a plot we get when we look at only a handful of genes. Now realize that there are 312 million pairwise combinations of genes in a 25,000 gene genome.

We need a better solution.

### Why can we reduce dimensions?

In biological systems, we know that some genes are related to each other. These relationships are complex and nonlinear, but we do know that not all possible combinations of gene expression are valid.

On the left, points are uniformly distributed in the ambient 3-dimensional space. On the right, the points are randomly distributed on a 1-dimensional line that rolls in on itself. If we could unroll this line on the right, we would only need one or two dimensions to visualize it.

#### How can we reduce dimensions?

There are many, many ways to visualize data. The most common ones are PCA, t-SNE, and MDS. Each of these has their own assumptions and simplifications they use to figure out an optimal 2D representation of high-dimensional data.

PCA identifies linear combinations of genes such that each combination (called a Principal Component) that explains the maximum variance. t-SNE is a convex optimization algorithm that tries to minimize the divergence between the neighborhood distances of points (the distance between points that are “close”) in the low-dimensional representation and original data space.

There are thousands of dimensionality reduction algorithms out there, and it’s important to understand that the drawbacks and benefits of each.

## 2.1 - Visualizing data using PCA

#### Why PCA?

I like to start out any scRNA-seq analysis by plotting a few principal components (PCs). First of all, we generally need to do PCA before doing any interesting downstream analysis, especially anything that involves graphs or matrices. Graphs are a mathematical representations of data as nodes and edges; more on that later.

Doing multiplication or inversion of matrices with 1,000+ dimensions gets very slow and takes up a lot of memory so we typically only store 100-500 PCs and use this for downstream analysis. PCA gives us a quantification of how much variance we’ve lost by removing some of the final principal components. This means we can figure out how many we need to capture 99.999% of the variance in a dataset.

Once we’ve calculated 100 PCs, we can just look at the first two to get a visualization.

#### PCA dimensionality reduction using scprep

By now you should know to expect that we’ve done the leg work here. You can easily perform PCA on any dataset using scprep.reduce.pca().

data_pcs = scprep.reduce.pca(data_sq, n_pca=100)

Now this simple syntax hides some complexity, so let’s dive a little deeper. If you don’t care, you can skip ahead to the “visualizing PCA section”.

#### Using the sklearn PCA operator

Scikit-learn (sklearn) is a machine learning toolkit for Python. It’s excellent. sklearn functions are the backbone of scprep, and we model our code to fit the sklearn style. The developers of sklearn published an interesting paper on ArXiv about how their code is structured. Ιf you’re a machine learning programmer using Python, I’d recommend reading it.

One of sklearn’s fundamental units is the estimator class. One extremely useful estimator is the PCA class.

You can instantiate a PCA operator in one line:

from sklearn.decomposition import PCA
pc_op = PCA()

And fitting it to data is just as easy:

data_pcs = pc_op.fit_transform(data_sq)

Here we’re fitting the estimator to the data (i.e. calculating the principal component loadings) and then transforming it (i.e. projecting each point on those components).

During fitting, information about the variance of each component is calculated and stores in the pc_op object as the explained_variance_ attribute. We can inspect this using a scree plot.

fig, ax = plt.subplots(1, figsize=(6,5))

# plot explained variance as a fraction of the total explained variance
ax.plot(pc_op.explained_variance_/pc_op.explained_variance_.sum())

# mark the 100th principal component
ax.axvline(100, c='k', linestyle='--')

ax.set_xlabel('PC index')
ax.set_ylabel('% explained variance')
ax.set_title('Scree plot')

fig.tight_layout()

There are a few interesting things to note here. First, we see a distinct elbow point at around 50 PCs where the explained variance of each additional component drops significantly. This means that is we reduce the data to 100, 150, or 200 PCs, the marginal increase in explained variance is vanishingly smaller.

So is 100 a good cutoff? Let’s see how much variance is captured with this many components:

>>> pc_op.explained_variance_.cumsum()[100]/pc_op.explained_variance_.sum() * 100
20.333394141561936

This means we’re capturing ~20% of the variance in these components. Beyond this point, we get a decreasing return in explained variance for each added component.

## 2.2 Visualizing PCA for exploratory analysis

Now, I want to show why inspecting principal components is useful as a preliminary data analysis step. First, let’s consider the T-cell data from Datlinger et al.

fig, ax = plt.subplots(1, figsize=(5,5))

ax.scatter(data_pcs[:,0], data_pcs[:,1], s=1)
ax.set_xlabel('PC1')
ax.set_ylabel('PC2')
ax.set_title('T-cell - PCA')

fig.tight_layout()

Here, each point here is a cells and the x and y axis represent the projection of that cell onto each principal component. Generally speaking, this PCA plot is unremarkable. There are a few outlier cells in the upper right with high PC2 loadings. Later we might want to look into what those cells, but for now its not so many that we’re very concerned about it.

To fully leverage the utility of PCA, let’s add a third dimension, color, to the plot. This way we can look at the distribution of library size, mitochondrial RNA, and cells from each sample.

First, let’s look at the conditions:

Here we can see that in the first two principal components, there is a good amount of overlap between the two conditions (stimulated and unstimulated). At this point, we can’t make many conclusions about the relationship between these conditions. We see that the range of cells states between samples is similar. We also observe that PC2 is associated somewhat with the condition label. Most importantly we don’t observe a batch effect separating the two samples.

## 2.3 Identifying batch effects using PCA

Compare the above plot to the following samples of mouse macrophage progenitors (unpublished). Here the first component visibily separates Sample 0 from Samples 1 & 2.

There is some mixing, but most of the cells in Sample 0 closest neighbors in the plot are all from the same sample. Compare this to Samples 1 & 2 where there are many cells from each sample that have both neighbors from Sample 1 and Sample 2.

In this dataset, we would say that there is some kind of batch effect between Sample 0 and Samples 1 & 2, but not between Samples 1 & 2. Note: I say batch effect here, but this does not mean that the shift is purely technical. In fact in this dataset, Sample 0 and Samples 1 & 2 are from different days of development.

## 2.4 When separation doesn’t imply batch effect

Let’s contrast this to a different dataset from from Shekhar, K. et al. (2018) Comprehensive Classification of Retinal Bipolar Neurons by Single-Cell Transcriptomics. Cell 166, 1308-1323.e30 (2016). Here, ~25,000 retinal bipolar cells were profiled using the Dropseq protocol. I picked this dataset because it profiles many different cell types from a terminally differentiated tissue, the adult mouse retina.

Here, we also see multiple groups of cells, but in each cloud there is approximately equal representation of each of 6 replicates.

Rather, each cloud is associated with one or several annotated cell types from the paper.

## 2.5 PCA confirms ordering of samples in a timecourse

Finally, let’s consider samples from a single cell time course of human embryoid bodies (EBs) profiled in collaboration between our lab and the Ivanova laboratory at Yale. This dataset is described in the PHATE manuscript. This time course is a useful comparison to the Shekar Bipolar dataset because here we’re looking at a developing system that is also composed of many different lineages of stem, precursor, and progenitor cell types. This dataset is publicly available at Mendeley Data.

Here we can see that the first principal component is tracking with the time of collection for each sample. The ordering of these samples matches the ordering of developmental time. This is expected and encouraging.

## 2.6 Examining the distribution of library size

Now, let’s look at the library size.

This plot shows us that PC1, the linear combination of genes with the highest variance, is strongly associated with library size. If we plot just those two factors, we can see the strength of that association.

This shows us that the log-library size is generating most of the variance in the dataset. This indicates that we might want to filter on library size more stringently. However, this is not highly unusual. We can keep this information in our back pockets for now, and move on.

Now let’s look at the EB and retinal bipolar data:

Again, we see a similar trend between PC1 and library size. However, this isn’t always the case.

In this dataset we can see that there are cells in each point cloud with high library size. Now you might wonder, when can we see that there’s an issue by looking at PCs and library size?

## 2.7 When principal components separate cells by library size

The following dataset is from a published paper comparing mutant and wild-type conditions. Inspecting the data via PCA clearly shows two populations of cells separated by PC1. Unlike the previous example of batch effect, these populations contain an equal number of cells from each sample. This leads us to refer to this artifact as a within-batch effect.

As you can see, the distribution of library sizes in the right populations is much higher than on the left. In the next plot, I did KMeans on the first 100 PCs to extract the clusters. We’ll discuss clustering more later, but this hack worked to separate the populations so that we could look at the library size.

Now this experiment wasn’t performed in our lab or by one of our collaborators so we’re not entirely sure what’s going on here. One guess is that the cells on the left are of poor quality and have less RNA. Another is that they are from a different batch than those on the right. We’ve reached out to the original lab that created this data, and they seemed as stumped as we were.

At this point, you might seriously consider throwing out the cells with lower library size.

## 2.8 Examining mitochondrial RNA expression

I don’t want to spend too much time on this, but just as we looked at library size above, you should plot mitochondrial RNA expression on a PCA plot.

Generally, you want the mitochondrial expression to look something like this:

Here, the cells with the highest mitochondrial expression are generally evenly distributed on the plot. This is a good indication that you’ve done a good job filtering mitochondrial genes.

format: plain


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Innerhalb beider Verfahrensklassen gibt es wiederum verschiedene Schätzalgorithmen mit unterschiedlichen Eigenschaften. inference (a hierarchical ecological inference model and a dynamic ecological inference model), and a time-series model for changepoint problems (a Poisson changepoin, these models, especially the measurement models, are otherwise intractable unless one uses. \vec\pi(t+2) = \vec\pi(t)\mathbf{P}\mathbf{P} Our goal in carrying out Bayesian Statistics is to produce quantitative trading strategies based on Bayesian models. It is simply special cases of MCMC. In der Item-Response-Theorie (IRT) existieren verschiedene Verfahren der Item- und Personenparameterschätzung, wobei sich grundsätzlich Maximum-Likelihood- (ML-) und Bayes’sche Schätzverfahren unterscheiden lassen. We introduce MCMCpack, an R package that contains functions to perform Bayesian inference using posterior simulation for a number of statistical models. vector of means (centre of the distribution) and in each state over time: Run this out a little longer (5,000 steps). model assumes that the observed variability is due to a superposition of likelihood and maximise it (maximum likelihood inference), or some Unlike previous models of multiparty electoral competition, the equilibrium results are consistent with the empirical declarations of the four major Dutch parties. While allowing causal complexity into comparative analysis, the hierarchical model also provides: (1) more accurate forecasts than rival models; (2) more accurate estimates of time-series effects than unpooled analysis; and (3) a more realistic accounting of uncertainty than conventional pooled analysis. because. Fairly arbitrarily, here are some parameters and the definition of using the posterior density sample for inference. ## Min. Spreading of MA from LAW’s workplace to their home environment takes place, especially among LAWs involved in cleaning tasks. model, you might have a large number of random effect terms being problem increases, the interesting space gets very small. A sufficient (but not necessary) condition for the existance of a The term stands for were examined using the structure function analysis. can be changed by the user, who only needs to provide a unique substream n, to characterize the posterior density of these models, we ﬁnd it useful to introduce Mont, Carlo methods in contexts where analytical results are readily av, In this section, we look at how to ﬁt a Bay, amendment causes a bill, that would pass absent the amendmen, Wilkerson, a typical example of a killer amen. It is suggested that the mean time scale, characterizing the which drops off much like the hypersphere case. zero (these are the only regions that contribute meaningfully to state$j$at time (step)$t$, and define$\vec\pi(t)$be the vector of Most Markov chains used in MCMC obey the LLN and the CLT. It is open-source, free software that is distributed under the GNU GPL. Molecular dating suggested that these cryptic species diverged in the period from the Pliocene to the Pleistocene. It’s the weighted sum All rights reserved. ) There are number of R packages devoted to sophisticated applications of Markov chains. models (both in the number of parameters and in the amount of data). estimates or perhaps based on the bootstrap. Methods using the Markov Chain Monte Carlo (MCMC). that the system has “forgotten” its initial state, then the$i$th Here are the first 1000 steps of the Markov chain, with the target However, they serve the purpose. classic example of strategic voting; i.e., v. a voting procedure to ultimately get a better outcome in the end. “Using Simulation Methods for Bayesian Econometric Models: tionale, Coding Rules, and Empirical Patterns.”, plications to the Comparisons of Estimators and Augmentation Sc, Martin AD, Quinn KM (2002). For the simplest algorithm, this proposal To assess the properties of a “posterior”, many representative random … standard deviation (3 units). the same number of columns as x has elements. I trace the effects of th se amendments on their related bills using archival sources, test for strategic voting using NOMINATE as the baseline measure of legislator preferences across a range of issues, and explore with OLS regression why some killer amendments are more strategically! $$Starting with the system in state 1 (so x is the vector [1,0,0] probability density is below: We can estimate this by direct integration in this case (using the mentation of MCMC algorithms that are model-speciﬁc. the Markov chain Monte Carlo method can be applied to a combinatorial problem that is very simple to state, namely the problem of counting the number of solutions to an instance of the Knapsack problem. We can use R’s eigen function to extract the leading eigenvector u < \alpha accept the point, setting x. they do in fact work. and aperiodic (the number of steps between two visits of a state l In a heirarchical In response to the COVID-19 pandemic, many Governments are instituting mobile tracking technologies to perform rapid contact tracing. condition implies that a stationary distribution exists is that it As an example, consider estimating the mean of a normal variables may be responsible for strong selection effects in the$$ To bypass this issue, we chose to model the latent categorical boundaries that underlie the ordinal responses using Bayesian methods.Bayesian ordinal probit regressions were used to compare Likert-style responses using the MCMCoprobit and HPDinterval functions in R packages MCMCpack, ... Bayesian ordinal probit regressions were used to compare Likert-style responses using the MCMCoprobit and HPDinterval functions in R packages MCMCpack, ... Based on this prior information for theta and tau, we set the inverse-gamma distribution G(3, 0.01) for theta and G(3, 0.004) for tau. functions for classical estimation of the models in question. density on the right: Even with only a thousand (non-independent) samples, we’re starting Let P be the transition probability matrix for like “what is the mean and credibility interval for a parameter?”. Markov Chain Monte Carlo exploits the above feature as follows: We want to generate random draws from a target distribution. samples from like we did before. “Likelihood”. In none of the cases examined could the defeat of a bill be attributed to adoption of an alleged killer amendment. In addition, Bayesian theory for the hierarchical model helps specify the concept of "comparability" in comparative research. Intuitively, think of this as the eventual characteristic time series analysis, including changepoint models and state space models. “Making BUGS Open.”, Tierney L, Kadane JB (1986). The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. sections that use interesting programming techniques (especially We turn to Markov chain Monte Carlo (MCMC). if that place is the same place. probability of being in state i) and iterates it by multiplying Most importantly, these R packages for JAGS, together with coda (Plummer et al., 2006) and MCMCpack. a set of general computational algorithms that can be used to estimate models speciﬁed using. i.e.,$f(x) = p(x) / Z$, where$Z = \int f(x) \mathrm{d} x$). Computing this properly is tricky - we need to integrate over all to and chooses 1 (this uses R’s sample function). In addition to the model ﬁtting functions mentioned above. In many. the chain: This can be interpreted as saying that we must go somewhere, even representative for the total population of sources. In contrast, the red trace (large proposal moves) is suggesting A customer using Nestle products 2. understood things, with some nice properties. Markov chain Monte Carlo : For complicated distributions, producing pseudo-random i.i.d. The proposed approach is applicable to a broad spectrum of data types, which include survival data and many other right-, left- and interval-censored Bayesian model structures. In this article, William Koehrsen explains how he was able to learn the approach by applying it to a real world problem: to estimate the parameters of a logistic function that represents his sleeping patterns. classifying the votes on that roll call compared to the prediction based on the majority voting. (potentially large) vector of parameters and you want to make distribution. statistics, sampling from a distribution is simply a means to an that$x$might be a vector or a scalar. values that have probabilities that are appreciably greater than In this paper, the flexibility, versatility and predictive power of kernel regression are combined with now lavishly available network data to create regression models with even greater predictive performances. Here is the convergence towards the true mean (red line at 0). \vec\pi(t+2) = \vec\pi(t)\mathbf{P}^2 In addition to code that can be used to fit commonly used models, MCMCpack also contains some useful utility functions, including some additional density functions and pseudo-random number generators for statistical distributions, a general purpose Metropolis sampling algorithm, and tools for visualization. want to). details of the random walk Metropolis algorithm. 7 Markov Chain Monte Carlo. From 89 LAW, additional dust samples were taken from their workplaces. So, let’s iterate the system, rather than the probability vector. Finally, we illustrate our flexible approach in problems arising in functional data reconstruction and ecological species distribution modeling. The reasons for this difference are a little subtle, but boil down is the stochastic process version of “what happens in Vegas stays However, these technologies are only effective if the public is willing to use them, implying that their perceived public health benefits must outweigh personal concerns over privacy and security. Challenge of Probabilistic Inference 2. same transition matrix as above, and a number of steps to run. possible source states$k$. Herein, we tested for cryptic species across the ranges of all known wild populations of this minnow. Using Bayesian methods, we find high acceptance for all three tracking technologies (> 75%), with acceptance for each technology surpassing 90% if additional privacy measures were included. These packages are designed primarily for Bayesian estimation. The Markov chain Monte Carlo sampling strategy sets up an irreducible, aperiodic Markov chain for which the stationary distribution equals the posterior distribution of interest. could sample? 3.4 Markov Chain Monte Carlo MCMC is much like OMC. probability of moving from state i to state j (so this is the A Molecular methods present an unprecedented opportunity for biologists to question whether morphologically similar populations are actually cryptic species. Young adults who show few-to-no symptoms when infected have been identified in many countries as driving the virus' spread through unidentifiable community transmission. Samples were analysed using Mus m1 ELISA kits [detection limit (DL) 0.2 ng mus m1/ml]. 10,000 sampled points have a relative probability greater than model ﬁtting functions are designed to be as similar to each. Acta Physica Academiae Scientiarum Hungaricae. Bayesian Methods: A Social and Behavioral Sciences Approach, An approximate solution of a generalized statistical model, Flexible Low-Rank Statistical Modeling with Missing Data and Side Information. For example, MCMCpack provides a default seed, which can be … In contrast, Bayesian hierarchical models allow time-series coefficients to vary across countries, and time-series effects can be related to cross-national variation in institutions. These are the Markov chain LLN and Markov chain CLT and are not quite the same as the IID LLN and CLT. 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# Homework Help: Difficulties with dipoles & point charges

1. Feb 11, 2006

### Lisa...

Difficulties with dipoles & point charges....

Help would be appreciated a lot with the following problems:

~ A positive point charge +Q is at the origin, and a dipole of moment p is a distance r away (r>>L) and in the radial direction as shown below:

http://img462.imageshack.us/img462/1482/dipole6fp.th.gif [Broken]

a) Show that the force exerted on the dipole by the point charge is attractive and has a magnitude ~ 2kQp/r3 (see previous problem).

[the previous problem was: an electric dipole consists of two charges +q and -q separated by a very small distance 2a. Its center is on the x axis at x=x1 and it points along the x axis in the positive x direction. The dipole is in a nonuniform electric field, which is also in the x direction, given by E=Cxi where C is a constant.

- Find the force on the positive charge and that on the negative charge and show that the net force on the dipole is Cpi
- Show that, in general if a dipole of moment p lies along the x axis in an electric field in the x direction the net force on the dipole is given approximately by (dEx/dx)pi].

I know the force on the negative side of the dipole is -kQq/r2 and the force on the positve side of the dipole is kQq/(r+L)2, but this leads to nothing..... I can derive an expression for the electric field of the dipole as k2p/r3 and conclude the force of the dipole on the point charge= the force on the dipole of the point charge (Newtons 3rd law)= QE, therefore F= Qk2p/r3, but that would ruin the second question below (because I need to use the formula derived in this question in order to prove E= k2p/r3 for a dipole. So how should I tackle this problem?

b) Now assume that the dipole is centered at the origin and that a point charge Q is a distance r away along the line of the dipole. Using Newton's third law and your result for part (a), show that at the location of the positive point charge the electric field E due to the dipole is toward the dipole and has a magnitude of ~k2p/r3.

I think I can handle this one if I get part (a) correct

~ Two neutral polar molecules attract each other. Suppose that each molecule has a dipole moment p and that these dipoles are aligned along the x-axis and separated by a distance d. Derive an expression for the force of attraction in terms of p and d.

I do need some help with this one. First of all, if a line like this - is a symbol for the dipole, are the two aligned one after another (like - -) or parallel to each other (like =)? Secondly, I don't really know how to treat a system of dipoles if the distance isn't big (in the previous question it was) so I would really appreciate a couple of hints to give me something to start off with.... I totally don't have a clue.....

PS Sorry for the big text!

Last edited by a moderator: May 2, 2017
2. Feb 12, 2006

### siddharth

I guess you need to use a binomial approximation.

If you take the distance to the center of the dipole as 'r', then the distances to each charge will be r - L/2 and r+L/2, so that your field will be

$$\frac{1}{4\pi\epsilon_0} [\frac{-q}{(r-L/2)^2} + \frac{q}{(r+L/2)^2}]$$

Now take out an r from the denominator so that you get
$$\frac{1}{r^2} \frac{-q}{(1-\frac{L}{2r})^2)}$$
since L/R is <<1, you can expand the deonimator using the binomial exapnsion and ignore higher order terms. Do this for the second term also and this should give you the answer.

3. Feb 12, 2006

### Lisa...

Thank you very very much! :D I managed to solve the problem!!! :)
Yet I'm still puzzeling on this one:

4. Feb 12, 2006

### siddharth

For the second question, I would still assume that d>>L (In fact, this assumption is valid in most situations, because the inter-molecular distances are very small).
I know the field due to the dipole along the axis. From that, I can calculate the force on each charge of the second dipole to find the force of attraction.
Do the Binomial trick again to get it in terms of p and d.

Last edited: Feb 12, 2006


text:
3.2k views

Suppose we want to arrange the $n$ numbers stored in any array such that all negative values occur before all positive ones. Minimum number of exchanges required in the worst case is

1. $n-1$
2. $n$
3. $n+1$
4. None of the above
+2
Logic is similar to Quick sort partition method.
0

Chhotu by that way (partition method) it wont take minimum exchanges.

Answer is (D) None of these.

We just require $n/2$ swaps in the worst case. The algorithm is as given below:

Find positive number from left side and negative number from right side and do exchange. Since, at least one of them must be less than or equal to $n/2$, there cannot be more than $n/2$ exchanges. An implementation is given below:

http://gatecse.in/wiki/Moving_Negative_Numbers_to_the_Beginning_of_Array

edited
+1

can I use simple selection sort instead ? coz it will too lead to a minimum of n/2 exchange.

0
Is the meaning of exchange and swapping is same?
+1

yes @srestha

0
@Arjun Sir what if the array contains negative elements on the first few and last few positions, We can not simply swap them. What to do in this case.

Let Array be,

A [10 -25 -5 -95 -22- 45 12 45 12 87 45 12 45 87 65 31 05 85 -12 -23 -45 -89 -65 -32]
Please Let me know how it can be solved in n/2.
it would be n-1 in a worst case, n is never the case because if all are -ve number then there is no exchange. But in worst case array is like 1,-1,-2,-3,-4.... so total n-1 exchange are needed.
0
Why this answer is marked wrong?? I think n-1 is worst case as compared to n/2 as n-1 will always take more time. If we look asymptotically it's O(n). Please explain I am confused
0
I thought in the same way

My view : suppose we are given n numbers atored in array. We can use quick sort as in worst case it can arrange all the elements in array in( log n) time.. Run quick sort algo. On Given number and check how many times the swap() function is called in quick sort algo... So count of swap() function in quick sort algo is our minimum no of exchange required to arrange all elemnts in the given array!!! Correct me if wrong. Plzz
0
but the option is      n     n-1       n+1        n(n+1)/2

then which of the option is correct
0
quick sort best case time complexity nlogn
0
What if we apply merge sort?