Model: Chandar/sv-subject-based-bert-base-uncased
Author: Chandar
Pipeline: sentence-similarity
Library: sentence-transformers
Tags: sentence-transformers, safetensors, bert, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:1124250, loss:CoSENTLoss, arxiv:1908.10084, base_model:google-bert/bert-base-uncased, base_model:finetune:google-bert/bert-base-uncased, model-index, text-embeddings-inference, endpoints_compatible, region:us
Base models (finetune): id: google-bert/bert-base-uncased
Card metadata: tags: sentence-transformers, sentence-similarity, feature-extraction, generated_from_trainer, dataset_size:1124250, loss:CoSENTLoss
base_model: google-bert/bert-base-uncased
widget: source_sentence: mason-wasp	is	solitary.
Thus	the	process	of	organic	evolution	is	far	from	being	fully	understood.	We	can
only	suppose	that	as	there	are	devised	by	human	beings	many	puzzles	apparently
unanswerable	till	the	answer	is	given,	and	many	necromantic	tricks	which	seem
impossible	till	the	mode	of	performance	is	shown;	so	there	are	apparently
incomprehensible	results	which	are	really	achieved	by	natural	processes.	Or,
otherwise,	we	must	conclude	that	since	Life	itself	proves	to	be	in	its	ultimate
nature	inconceivable,	there	is	probably	an	inconceivable	element	in	its	ultimate
workings.
END	OF	VOL.	I.
sentences: 988 CHAPTER 34 | ANIMAL NUTRITION AND THE DIGESTIVE SYSTEM
This content is available for free at http://cnx.org/content/col11448/1.9, Cellular Communication in Yeasts
The first life on our planet consisted of single-celled prokaryotic organisms that
had limited interaction with each other. While some external signaling occurs between
different species of single-celled organisms, the majority of signaling within bacteria and
yeasts concerns only other members of the same species. The evolution of cellular
communication is an absolute necessity for the development of multicellular organisms,
and this innovation is thought to have required approximately 2.5 billion years to appear in
early life forms.
Yeasts are single-celled eukaryotes, and therefore have a nucleus and organelles
characteristic of more complex life forms. Comparisons of the genomes of yeasts,
nematode worms, fruit flies, and humans illustrate the evolution of increasingly complex
signaling systems that allow for the efficient inner workings that keep humans and other
complex life forms functioning correctly.
Kinases are a major component of cellular communication, and studies of these
enzymes illustrate the evolutionary connectivity of different species. Yeasts have 130 types
of kinases. More complex organisms such as nematode worms and fruit flies have 454
and 239 kinases, respectively. Of the 130 kinase types in yeast, 97 belong to the 55
subfamilies of kinases that are found in other eukaryotic organisms. The only obvious
deficiency seen in yeasts is the complete absence of tyrosine kinases. It is hypothesized
that phosphorylation of tyrosine residues is needed to control the more sophisticated
functions of development, differentiation, and cellular communication used in multicellular
organisms.
Because yeasts contain many of the same classes of signaling proteins as humans,
these organisms are ideal for studying signaling cascades. Yeasts multiply quickly and
are much simpler organisms than humans or other multicellular animals. Therefore, the
signaling cascades are also simpler and easier to study, although they contain similar
counterparts to human signaling.
[2]
Watch thiscollection (http://openstaxcollege.org/l/bacteria_biofilm) of interview clips with biofilm
researchers in “What Are Bacterial Biofilms?”
2. G. Manning, G.D. Plowman, T. Hunter, S. Sudarsanam, “Evolution of Protein Kinase Signaling from Yeast to
Man,” Trends in Biochemical Sciences 27, no. 10 (2002): 514–520.
266 CHAPTER 9 | CELL COMMUNICATION
This content is available for free at http://cnx.org/content/col11448/1.9, size,	and	commonly	with	organizations	more	or	less	advanced;	and	that
throughout	each	organic	sub-kingdom,	there	is	a	certain	general,	though
irregular,	relation	between	the	initial	and	the	final	bulks.	Vegetals	exhibit	this
relation	less	manifestly	than	animals.	Yet	though,	among	the	plants	that	begin
life	as	minute	spores,	there	are	some	which,	by	the	aid	of	an	intermediate	form,
grow	to	large	sizes,	the	immense	majority	of	them	remain	small.	While,
conversely,	the	great	Monocotyledons	and	Dicotyledons,	when	thrown	off	from
their	parents,	have	already	the	formed	organs	of	young	plants,	to	which	are
attached	stores	of	highly	nutritive	matter.	That	is	to	say,	where	the	young	plant
consists	merely	of	a	centre	of	development,	the	ultimate	growth	is	commonly
insignificant;	but	where	the	growth	is	to	become	great,	there	exists	to	start	with,
a	developed	embryo	and	a	stock	of	assimilable	matter.	Throughout	the	animal
kingdom	this	relation	is	tolerably	manifest	though	by	no	means	uniform.	Save
among	classes	that	escape	the	ordinary	requirements	of	animal	life,	small	germs
or	eggs	do	not	in	most	cases	give	rise	to	bulky	creatures.	Where	great	bulk	is	to
be	reached,	the	young	proceeds	from	an	egg	of	considerable	bulk,	or	is	born	of
considerable	bulk	ready-organized	and	partially	active.	In	the	class	Fishes,	or	in
such	of	them	as	are	subject	
to	similar	conditions	of	life,	some	proportion	usually
obtains	between	the	sizes	of	the	ova	and	the	sizes	of	the	adult	individuals;
though	in	the	cases	of	the	sturgeon	and	the	tunny	there	are	exceptions,	probably
determined	by	the	circumstances	of	oviposition	and	those	of	juvenile	life.
Reptiles	have	eggs	that	are	smaller	in	number,	and	relatively	greater	in	mass,
than	those	of	fishes;	and	throughout	this	class,	too,	there	is	a	general	congruity
between	the	bulk	of	the	egg	and	the	bulk	of	the	adult	creature.	As	a	group,	birds
show	us	further	limitations	in	the	numbers	of	their	eggs	as	well	as	farther
increase	in	their	relative	sizes;	and	from	the	minute	eggs	of	the	humming-bird	up
to	the	immense	ones	of	the	
Epiornis
,	holding	several	quarts,	we	see	that,
speaking	generally,	the	greater	the	eggs	the	greater	the	birds.,	Finally,	among
mammals	 (omitting	 the	 marsupials)	 the	 young	 are	 born,	 not	 only	 of
comparatively	large	sizes,	but	with	advanced	organizations;	and	throughout	this
sub-division	of	the	
Vertebrata
,	as	throughout	the	others,	there	is	a	manifest
connexion	between	the	sizes	at	birth	and	the	sizes	at	maturity.	As	having	a
kindred	meaning,	there	must	finally	be	noted	the	fact	that	the	young	of	these
highest	animals,	besides	starting	in	life	with	bodies	of	considerable	sizes,	almost
fully	organized,	are,	during	subsequent	periods	of	greater	or	less	length,	supplied
with	nutriment—in	birds	by	feeding	and	in	mammals	by	suckling	and	afterwards
by	feeding.	So	that	beyond	the	mass	and	organization	directly	bequeathed,	a	bird
or	mammal	obtains	a	further	large	mass	at	but	little	cost	to	itself., source_sentence: mason-wasp	is	solitary.
Thus	the	process	of	organic	evolution	is	far	from	being	fully	understood.	We	can
only	suppose	that	as	there	are	devised	by	human	beings	many	puzzles	apparently
unanswerable	till	the	answer	is	given,	and	many	necromantic	tricks	which	seem
impossible	till	the	mode	of	performance	is	shown;	so	there	are	apparently
incomprehensible	results	which	are	really	achieved	by	natural	processes.	Or,
otherwise,	we	must	conclude	that	since	Life	itself	proves	to	be	in	its	ultimate
nature	inconceivable,	there	is	probably	an	inconceivable	element	in	its	ultimate
workings.
END	OF	VOL.	I.
sentences: hearing	not	being	called	for,	large	ears	gave	no	greater	advantage	than	small
ones.	Would	an	individual	with	smaller	ears	than	usual,	survive	and	propagate
better	than	other	individuals,	in	consequence	of	the	economy	of	nutrition
achieved?	To	suppose	this	is	to	suppose	that	the	saving	of	a	grain	or	two	of
protein	per	day	would	determine	the	kangaroo's	fate.
Long	ago	I	discussed	this	matter	in	the	
Principles	of	Biology
	(§	166),	taking	as
an	instance	the	decrease	of	the	jaw	implied	by	the	crowding	of	the	teeth,	and
now	proved	by	measurement	to	have	taken	place.	Here	is	the	passage
:—
"No	functional	superiority	possessed	by	a	small	jaw	over	a	large	jaw,	in
civilized	life,	can	be	named	as	having	caused	the	more	frequent	survival	of
small-jawed	individuals.	The	only	advantage	which	smallness	of	jaw	might
be	supposed	to	give,	is	the	advantage	of	economized	nutrition;	and	this
could	not	be	great	enough	to	further	the	preservation	of	men	possessing	it.
The	decrease	of	weight	in	the	jaw	and	co-operative	parts	that	has	arisen	in
the	course	of	many	thousands	of	years,	does	not	amount	to	more	than	a	few
ounces.	This	decrease	has	to	be	divided	among	the	many	generations	that
have	lived	and	died	in	the	interval.	Let	us	admit	that	the	weight	of	these
parts	diminished	to	the	extent	of	an	ounce	in	a	single	generation	(which	is	a
large	admission);	it	still	cannot	be	contended	that	the	having	to	carry	an
ounce	less	in	weight,	or	having	to	keep	in	repair	an	ounce	less	of	tissue,
could	sensibly	affect	any	man's	fate.	And	if	it	never	did	this—nay,	if	it	did
not	cause	a	
frequent
	survival	of	small-jawed	individuals	where	large-jawed
individuals	died,	natural	selection	could	neither	cause	nor	aid	diminution	of
the	jaw	and	its	appendages."
When	writing	this	passage	in	1864,	I	never	dreamt	that	a	quarter	of	a	century
later,	the	supposable	cause	of	degeneration	here	examined	and	excluded	as
impossible,	would	be	enunciated	as	an	actual	cause	and	named	"reversed
selection."
One	of	the	arguments	used	to	show	the	adequacy	of	natural	selection	under	its
direct	or	indirect	form	consists	of	a	counter-argument	to	the	effect	that
inheritance	of	functionally-wrought	changes,	supposing	it	to	be	operative,	does
not	explain	certain	of	the	facts.	This	is	alleged	by	Prof.	Weismann	as	a	part
justification	for	his	doctrine	of	Panmixia.	Concerning	the	"blind	fish	and
amphibia"	found	in	dark	places,	which	have	but	rudimentary	eyes	"hidden	under, 312 
 
Table 14.1 
 
The table compares properties (lengths, copy number, functions, percent age of the genome, 
location in the genome,  etc.) of repetitive -sequence DNAs. The fact  most of a eukaryotic 
genome is made up of repeated DNA and that transposons can be as much as 80% of a 
genome—came as a surprise! We’ll focus next on the different kinds of transposable elements. 
 240 Identifying Different Kinds of DNA Each CoT Fraction   
 241 Some Repetitive DNA Functions  
 
14.3  The “Jumping Genes” of Maize 
 
Barbara McClintock’s report that bits of DNA could jump a round and integrate into new loci in 
DNA was so dramatic and arcane that many thought the phenomenon was either a one -off or 
not real!  Only with the  subsequent discovery of transposons in  bacteria (and in other 
eukaryotes) were McClintock’s jumping genes finally recognized for what they were.  
To begin the tale, let’s look at the maize reproduction in Figure 14.7 (below)., CHAPTER 3. RADIATIVE PROCESSES IN ASTROPHYSICS 128
3.4 Radiation hydrodynamics
We can now integrate the two previous moments equations over the frequency. We obtain the
frequency integrated radiation energy equation as
@Erad
@t + rFrad = 4
Z +1
0
jd, source_sentence: mason-wasp	is	solitary.
Thus	the	process	of	organic	evolution	is	far	from	being	fully	understood.	We	can
only	suppose	that	as	there	are	devised	by	human	beings	many	puzzles	apparently
unanswerable	till	the	answer	is	given,	and	many	necromantic	tricks	which	seem
impossible	till	the	mode	of	performance	is	shown;	so	there	are	apparently
incomprehensible	results	which	are	really	achieved	by	natural	processes.	Or,
otherwise,	we	must	conclude	that	since	Life	itself	proves	to	be	in	its	ultimate
nature	inconceivable,	there	is	probably	an	inconceivable	element	in	its	ultimate
workings.
END	OF	VOL.	I.
sentences: & Zhu, G.L. (2006). Critical radius and dipole
polarizability for a conﬁned system. Chin. Phys., 15, 1172-1176.
Bitensky, I.S.; Ferleger, V .K. & Wojciechowski, I.A. (1997). Distortion of H 2 potentials by
embedding into an electron gas at molecule scattering by a metal surface. Nucl. Instr.
and Methods in Phys. Res. B, 125, 201-206.
Jia, C.S.; Wang, J.Y.; He, S. & Sun, L.T. (2000). Shape invariance and the supersymmetry WKB
approximation for a diatomic molecule potential. J. Phys. A, 33, 6993-6998.
Olson, J.A. & Micha, D.A. (1978). Transition operators for atomâ ˘A¸Satom potentials: The
Hilbertâ ˘A¸SSchmidt expansion. J. Chem. Phys., 68, 4352.
Varshni, Y.P . (1990). Eigenenergies and oscillator strengths for the Hulthen potential.Phys. Rev.
A, 41, 4682-4689.
Filho, E.D. & Ricotta, R.M. (1995). Supersymmetry, variational method and Hulthen potential.
Mod. Phys. Lett. A, 10, 1613-1618.
Qian, S.W.; Huang, B.W. & Gu, Z.Y. (2002). Supersymmetry and shape invariance of the
effective screened potential. New J. Phys., 4, 13.1.
Greene, R.L. & Aldrich, C. (1976). Variational wave functions for a screened Coulomb
potential. Phys. Rev. A, 14, 2363-2366.
251Application of the Nikiforov-Uvarov Method in Quantum Mechanics, Those	slow	alternations	of	elevation	and	subsidence	which	take	place	over
immense	areas,	here	producing	a	continent	where	once	there	was	a	fathomless
ocean,	and	there	causing	wide	seas	to	spread	where	in	a	long	past	epoch	there
stood	snow-capped	mountains,	gradually	work	great	atmospheric	changes.	While
the	highest	parts	of	an	emerging	surface	of	the	Earth's	crust	exist	as	a	cluster	of
islands,	the	plants	and	animals	which	in	course	of	time	migrate	to	them	have
climates	that	are	peculiar	to	small	tracts	of	land	surrounded	by	large	tracts	of
water.	As,	by	successive	upheavals,	greater	areas	are	exposed,	there	begin	to
arise	sensible	contrasts	between	the	states	of	their	peripheral	parts	and	their
central	parts.	The	breezes	which	daily	moderate	the	extremes	of	temperature
near	the	shores,	cease	to	affect	the	interiors;	and	the	interiors,	less	qualified	too
in	their	heat	and	cold	by	such	ocean-currents	as	approach	the	coast,	acquire	more
decidedly	the	characters	due	to	their	latitudes.	Along	with	the	further	elevations
which	unite	the	members	of	the	archipelago	into	a	continent,	there	come	new
meteorologic	changes,	as	well	as	exacerbations	of	the	old.	The	winds,	which
were	comparatively	uniform	in	their	directions	and	periods	when	only	islands
existed,	grow	involved	in	their	distribution,	and	widely-different	in	different
parts	of	the	continent.	The	quantities	of	rain	which	they	discharge	and	of
moisture	which	they	absorb,	vary	everywhere	according	to	the	proximity	to	the
sea	and	to	surfaces	of	land	having	special	characters.
Other	complications	result	from	variations	of	height	above	
the	sea:	elevation
producing	a	decrease	of	heat	and	consequently	an	increase	in	the	precipitation	of
water—a	precipitation	which	takes	the	shape	of	snow	where	the	elevation	is	very
great,	and	of	rain	where	it	is	not	so	great.	The	gatherings	of	clouds	and	descents
of	showers	around	mountain	tops,	are	familiar	to	every	tourist.	Inquiries	in	the
neighbouring	valleys	prove	that	within	distances	of	a	mile	or	two	the	recurring
storms	differ	in	their	frequency	and	violence.	Nay,	even	a	few	yards	off,	the
meteorological	conditions	vary	in	such	regions:	as	witness	the	way	in	which	the
condensing	vapour	keeps	eddying	round	on	one	side	of	some	high	crag,	while
the	other	side	is	clear;	or	the	way	in	which	the	snowline	runs	irregularly	to
different	heights,	in	all	the	hollows	and	ravines	of	each	mountain	side.
As	climatic	variations	thus	geologically	produced,	are	compounded	with	those
which	result	from	slow	astronomical	changes;	and	as	no	correspondence	exists
between	the	geologic	and	the	astronomic	rhythms;	it	results	that	the	same	plexus
of	actions	never	recurs.	Hence	the	incident	forces	to	which	the	organisms	of
every	locality	are	exposed	by	atmospheric	agencies,	are	ever	passing	into, 224 
 
The result of polyadenylation is a 3 ’ poly(A) tail whose functions include assisting in 
the transit of mRNAs from the nucleus  and regulating the half-life of mRNAs in the cytoplasm. 
The poly(A) tail shortens each time a ribosome finishes translating the mRNA.  
 198 mRNA 5’ Capping and 3’ Polyadenylation  
 
 
 
10.5 Ribosomal RNA Processing in Eukaryotic Nuclei 
 
In most eukaryotes, a large rRNA  gene transcribes a 45S precursor transcript containing (from 
shortest to longest) 5.8S rRNA , 18S rRNA  and 28S rRNA. The S comes from  Theodor 
Svedberg, the biochemist who developed the sedimentation velocity ultra-centrifugation 
technique to separate molecules like RNA by size. The higher the S value , the larger the 
molecule and therefore the faster it moves through the viscous sugar gradient during 
centrifugation. RNA polymerase I transcrib es 45S precursor rRNAs (pre -RNAs) from multiple 
large transcription units in the genome. One such unit is shown in Figure 10.21. 
 
 
Fig. 10.21: The 45S eukaryotic rRNA genes  (1) encode the 18S, 5.8S and 28S ribosomal RNAs ( 2). Pre-
rRNA transcripts contains the rRNAs (3). Hydrolytic cleavage of the pre -rRNA (3) will separate the rRNAs 
and specific rRNA nucleases will hydrolyze spacer and flanking RNA, leaving behind mature rRNAs (4).  
CHALLENGE: Bacterial mRNAs have been found with very short poly(A) 
tails. Would you expect poly(A) tails on bacterial mRNAs to function the 
same way they do in eukaryotic cells? Explain your expectation., source_sentence: mason-wasp	is	solitary.
Thus	the	process	of	organic	evolution	is	far	from	being	fully	understood.	We	can
only	suppose	that	as	there	are	devised	by	human	beings	many	puzzles	apparently
unanswerable	till	the	answer	is	given,	and	many	necromantic	tricks	which	seem
impossible	till	the	mode	of	performance	is	shown;	so	there	are	apparently
incomprehensible	results	which	are	really	achieved	by	natural	processes.	Or,
otherwise,	we	must	conclude	that	since	Life	itself	proves	to	be	in	its	ultimate
nature	inconceivable,	there	is	probably	an	inconceivable	element	in	its	ultimate
workings.
END	OF	VOL.	I.
sentences: Clin Interv Aging. 2006;1(3):253 -60. doi: 10.2147/ciia.2006.1.3.253. 
PMID: 18046878; PMCID: PMC2695176 
25. Chen G, Yung R. Meta -inflammaging at the crossroad of geroscience. Aging Med 
(Milton). 2019 Sep 8;2(3):157 -161. doi: 10.1002/agm2.12078. PMID: 31942529; 
PMCID: PMC6880720 
26. Fu C, Li Z, Mao Z. Association between Social Activ ities and Cognitive Function among 
the Elderly in China: A Cross -Sectional Study. Int J Environ Res Public Health. 2018 Jan 
30;15(2):231. doi: 10.3390/ijerph15020231. PMID: 29385773; PMCID: PMC5858300 
27. Upadhayay N, Guragain S. Comparison of cognitive functi ons between male and 
female medical students: a pilot study. J Clin Diagn Res. 2014 Jun;8(6):BC12 -5. doi:, Application of the Nikiforov-Uvarov Method in Quantum Mechanics 25
Substituting the double roots of k± into Eq.(170), the four possible forms of the π(s) for either
k+ or k− are derived as follows
π(s)= −s
2 ± 1
2
⎧
⎨
⎩
[(
2√α −√1 + 4γ
)
s −2√α
]
for k+ = β −γ +
√
α(1 + 4γ)
[(
2√α + √1 + 4γ
)
s −2√α
]
for k− = β −γ −
√
α(1 + 4γ).
(173)
In order to obtain a physical solution we have to ensure that the polynomial τ(s)= ˜τ(s)+
2π(s) must satisfy a negative derivative. For this reason, we select the π(s);
π(s)= −s
2 − 1
2
[(
2
√
α +
√
1 + 4γ
)
s −2
√
α
]
, (174)
for k− = β −γ −
√
α(1 + 4γ). The following track in this selection is to achieve the condition
τ′(s) < 0. Therefore τ(s) is written
τ(s)= 1 −2s −
[(
2
√
α +
√
1 + 4γ
)
s −2
√
α
]
, (175)
and then its negative derivative becomes
τ′(s)= −(2 + 2
√
α +
√
1 + 4γ) < 0. (176)
We can also write down the λ = k− + π′(s) and λn = −nτ′(s) −n(n −1)σ′′(s)/2, keeping in
our mind that λ = λn ;
λ = β −γ − 1
2 (1 + 2
√
α)
(
1 +
√
1 + 4γ
)
= n
[
1 + 2
√
α + n +
√
1 + 4γ
]
, n = 0, 1, 2, ....
(177)
After bring back α, β and γ which are deﬁned in Eq.(168) and simple manipulations, we have
the energy spectrum of the Hulthen potential (Agboola, 2011)
E = −¯h2
2μ
[
(Kμ/¯h2)
n + ℓ+ 1 − n + ℓ+ 1
2κ
]2
. (178)
If we take into account the limitation of κ → ∞, we have En = − μ
2¯h2 [K/(n + ℓ+ 1)]2. This is
the energy spectrum of the Coulomb potential we have investigated in Section 4.2.
We can now apply the relationships given by Eq.(7) and Eq.(27) through Eq.(28) to obtain the
wavefunctionψ(s). Therefore, the relevant polynomials are given
φ(s)= s
√α(1 −s)ℓ+1, (179)
ρ(s)= s2√α(1 −s)2ℓ+1, (180)
yn (s)= Bn s−2√α(1 −s)−(2ℓ+1) dn
dsn
[
sn+2√α(1 −s)n+2ℓ+1
]
≡ P(2√α,2 ℓ+1)
n (1 −2s). (181)
249Application of the Nikiforov-Uvarov Method in Quantum Mechanics, References 859
669. Raggio, G.A. (1981). States and composite systems in W*-algebras quantum mechanics. PhD
Thesis, ETH Z¨urich.
670. Raggio, G.A. (1988). A remark on Bell’s inequality and decomposable normal states. Letters
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672. Raggio, G.A., Werner, R.F. (1991). The Gibbs variational principle for inhomogeneous mean
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674. Raynaud, G. (2014). Fibered Contextual Quantum Physics. PhD Thesis, University of Birm-
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676. Reed, M., Simon, B. (1972). Methods of Modern Mathematical Physics. Vol I. Functional
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679. R ´edei, M. (2005a). John von Neumann on mathematical and axiomatic physics. The Role of
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680. R ´edei, M. (2005b). John von Neumann: Selected Letters . Providence: American Mathe-
mematical Society.
681. Renault, J. (1980). A Groupoid Approach to C*-algebras.Berlin: Springer.
682. R ´enyi, A. (1955). On a new axiomatic theory of probability. Acta Mathematica Academiae
Scientiarum Hungaricae 6, 286–335.
683. Rhodes, R. (1995). Dark Sun: The Making of the Hydrogen Bomb. New York: Touchstone.
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Functional Analysis 162, 287–312.
685. Rieckers, A. (1984). On the classical part of the mean ﬁeld dynamics for quantum lattice
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686. Rieffel, M.A. (1989). Deformation quantization of Heisenberg manifolds. Communications
in Mathematical Physics 122, 531–562.
687. Rieffel, M.A. (1990). Lie group convolution algebras as deformation quantizations of linear
Poisson structures. American Journal of Mathematics 112, 657–686.
688. Rieffel, M.A. (1994). Quantization and C∗-algebras. Contemporary Mathematics 167, 66–
97.
689. Riesz, F. (1907a). Sur les syst `emes orthogonaux des functions. Comptes Rendus de
l’Acad´emie des Sciences 144, 615–619.
690. Riesz, F. (1913). Les Syst `emes d’ ´Equations Lin ´eaires `a une Inﬁnit ´e d’Inconnues . Paris:
Gauthiers–Villars.
691. Riesz, F. (1934)., source_sentence: mason-wasp	is	solitary.
Thus	the	process	of	organic	evolution	is	far	from	being	fully	understood.	We	can
only	suppose	that	as	there	are	devised	by	human	beings	many	puzzles	apparently
unanswerable	till	the	answer	is	given,	and	many	necromantic	tricks	which	seem
impossible	till	the	mode	of	performance	is	shown;	so	there	are	apparently
incomprehensible	results	which	are	really	achieved	by	natural	processes.	Or,
otherwise,	we	must	conclude	that	since	Life	itself	proves	to	be	in	its	ultimate
nature	inconceivable,	there	is	probably	an	inconceivable	element	in	its	ultimate
workings.
END	OF	VOL.	I.
sentences: 11.4 The Flea on Schr ¨odinger’s Cat 455
where M = Nm is the total mass of the system, for simplicity we assumed V to be
analytic (it will even be taken to be polynomial), and we abbreviated
fk(ρ)=
(
− 1√
N′
N
∑
l=1
ρl
)k
+
N
∑
n=1
(
√
N′ρn − 1√
N′
N
∑
l=1
ρl
)k
. (11.22)
Note that f1(ρ)= 0, so that to lowest order (i.e. k = 2) we have
hAE (Q,ρ)=
(
1
2 N
N
∑
n=1
ρ2
n −
N
∑
k̸=l
ρkρl
)
V ′′(Q)+ ··· (11.23)
We pass to the corresponding quantum-mechanical Hamiltonians in the usual way,
and couple a two-level quantum system to the apparatus through the Hamiltonian
hSA = μ·σ3 ⊗P, (11.24)
where the object observable s = σ3, acting on HS = C2, is to be measured. The idea
is that hA is the Hamiltonian of a pointer that registers outcomes by localization on
the real line, hE is the (free) Hamiltonian of the “environment”, realized as the in-
ternal degrees of the freedom of the total apparatus that are not used in recording
the outcome of the measurement, and hAE describes the pointer-environment inter-
action. The classical description of the apparatus then involves two approximations:
• Ignoring all degrees of freedom except those of A, which classically are (P,Q);
• Taking the classical limit of hA, here realized as N →∞ (in lieu of ¯h →0).
The measurement ofs is now expected to unfold according to the following scenario:
1. The apparatus is initially in a metastable state (this is a very common assump-
tion), whose wave-function is e.g. a Gaussian centered at the origin.
2. If the object state is “spin up”, i.e., ψS =( 1,0), then it kicks the pointer to the
right, where it comes to a standstill at the bottom of the double well. If spin is
down, likewise to the left. IfψS =( 1,1)/
√
2, the pointer moves to a superposition
of these, which is close to the ground state of V displayed in Figure 11.2.
3. In the last case, the Flea mechanism of §10.2 comes into play: tiny asymmetric
perturbations irrelevant for small N localize the ground state as N →∞.
4. Mere localization of the ground state of the perturbed (apparatus) Hamiltonian in
the classical regime is not enough: there should be a dynamical transition from
the ground state of the original (unperturbed) Hamiltonian (which has become
metastable upon perturbation) to the ground state of the perturbed one. This dy-
namical mechanism in question should also recover the Born rule.
Thus the classical description of the apparatus is at the same time the root of the
measurement problem and the key to its solution: it creates the problem because at
ﬁrst sight a Schr¨odinger Cat state has the wrong classical limit (namely a mixture),
but it also solves it, because precisely in the classical limit Cat states are destabilized
even by the tiniest (asymmetric) perturbations and collapse to the “right” states., 10.9 The Goldstone Theorem 421
where the sum overa (implicit in the Einstein summation convention) ranges from 1
to M, v = ∥ϕc∥, and the ﬁelds χ =( χ1,..., χN−M) are chosen orthogonal (in RN )t o
each Taϕc, a = 1,..., M, and hence to the θa. Provided that the generators of SO(N)
(and hence of G ⊂SO(N)) have been chosen such that
⟨Taϕc,Tbϕc⟩= v2δab, (10.331)
the ﬁelds θa deﬁned by (10.330) coincide with the ﬁelds in (10.328) up to quadratic
terms in χ and θ; to see this, expand the exponential and also use the fact that both
⟨Taϕc,ϕc⟩and ⟨Taϕc,χ⟩vanish. This transformation is only well deﬁned if v ̸=0,
i..e., if SSB from G to H occurs, and its existence implies the Goldstone Theorem
10.26, for by (10.330) and G-invariance, V (ϕ) is independent of θ.
The Goldstone Theorem can be derived in quantum ﬁeld theory, but in the spirit
of this chapter we will discuss it rigorously for quantum spin systems. Far from
considering the most general case, we merely treat the simplest setting. We assume
thatA is a quasi-local C*-algebra given by (8.130), with H = Cn. Furthermore:
1. The group of space translations Zd acts on A by automorphisms τx, and so does
the group Rof time translations by automorphismsαt commuting with the τx (cf.
§9.3); we often write α(x,t) for αt ◦τx as well as a(x,t) for αt ◦τx(a).
2. A compact Lie group G acts on H = Cn through a unitary representation u and
hence acts on on A by automorphisms γg as in (10.58) - (10.59), such that
γg ◦α(x,t) = α(x,t) ◦γg ((x,t) ∈Zd ×R,g ∈G). (10.332)
3. There exists a pure translation-invariant ground state ω.
4. One has SSB in that ω◦γg ̸=ω for all g ∈Ga ⊂G, where
Ga = {exp(sTa),s ∈R,Ta ∈g}. (10.333)
5. There is an n-tuple ϕ =( ϕ1,..., ϕn) of local operators ϕα ∈Mn(C) that trans-
forms under G by ϕ ↦→ugϕu∗
g = γg(ϕ), and deﬁnes an order parameter φa by
φa = δaϕ ≡ d
ds
(
γexp(sTa)(ϕ)
)
|s=0 , (10.334)
at least for SSB of Ga (as above) in that, cf. Deﬁnition 10.6,
ω(δaϕ) ̸=0. (10.335)
6. Writing j0
a = iu′(Ta) ∈Mn(C), it follows that δaϕ = −i[ j0
a,ϕ], and hence that
δaϕ(x)= −i lim
Λ↗ Zd ∑
y∈Λ
[ j0
a(y),ϕ(x)] (x ∈Zd), (10.336)
since by (8.132) (i.e., Einstein locality) only the termy = x will contribute. Physi-
cists then wish to deﬁne a charge by Qa = ∑y∈Zd j0
a(y) and write (10.336) as
δaϕ(x)= −i[Qa,ϕ(x)],b u tQa does not exist precisely in the case of SSB !, tration,p.115).Thebaby'sparentshavealreadyattainedtheirfullgrowth.Theamountoffoodthatapersonneedstomakeupfortheheatradiatedfromthesurfaceofthebodyvariesw^iththesizeandalsow^iththeshapeofthebody(seeillustrationopposite).Thesmallerachild,themoresurfacehehasinproportiontohisbodyweight,andhencehelosesrelativelymoreheat.Byactualmeasurement,aone-year-oldchildneedsapproximatelytwiceasmuchenergyperpoundofbody-weightasdoesanadult.Energyneedsareindirectlyrelatedtosex.Girlsandwomenhaveathickerlayeroffattytissuebeneaththeskinthanboysandmen.Thisfatpreventsrapidradiationofheatfromthebody.Itisinterestingtorecallthatmostlong-distanceswimmingrecordsareheldbywomenratherthanbymen.Exposurealsoaffectsthebody'slossofheat.Thebodylosesheatfasterinacold,dry,windyclimatethaninawarm,moistclimate.Cloth-ingandshelterare,ofcourse,factorsinthelossofheat.Circulationoftheblood,breathing,andotherprocessesarecontinuallygoingonwhenthebodyisatrest."Warm-blooded"animalsmaintainaconstanttemperature.Theheatcontinuallyradiatingfromthesurfaceisconstantlybeingreplaced.Muscularmovementsarecontinuallytakingplaceinthedigestiveorgans,andenergyisusedinvariousotherwayswithinthebody.From40to50percentofthebodyismadeupofmus-culartissue.Thebulkofthistissueisattachedtotheskeletonandisusedinstandingaswellasinlocomotionandothervoluntaryactions.Atalltimes,evenwhenthesemusclesarerelaxed,energyisusedinkeepingthemsomewhatonthestretch.AbovetheBaseLineTheamountofenergythatthebodyuses,evenwhileitis"doingnothing",isconstantlyinfluencedbytwosetsoffactors.Digestingfoodinvolvesameasurableamountofenergy.Thusthebodyusesabout6percentmoreenergysoonafterameal,whenthedigestiveorgansaremostactive,thanjustbeforeameal,whendigestionispracti-callyatastandstill.Whenyouaresittingandreading,orwhenyouarestandingquietly,yourbodyusesaboutone-and-a-thirdtimesasmuchenergyasitdoeswhilesleeping.Walkingatamoderatepaceusesabouttwo-and-a-halftimesasmuch;runningusesaboutseventimesandstair-climbingaboutfifteentimesasmuch.UnitofEnergyTomeasuretheenergyexpendedbythelivingbody,weuseaunitdevelopedbyengineers.ThisistheCalorie(Cal),and,likethemorefamiliarfoot-pound(ft-lb)usedinmeasuringwork,itiscomposedoftwofactors.Wemeasureworkasifitalwaysconsistedofsomequantityofmatter(pounds)movingacertaindistance(feet).Inasimilarwaywemeasureheatasaquantityofmatter,forexample,1kilogram(kg)ofwater,beingheatedacertain"distance"(1degreeonthecentigradescale).116
pipeline_tag: sentence-similarity
library_name: sentence-transformers
metrics: cosine_accuracy, cosine_accuracy_threshold, cosine_f1, cosine_f1_threshold, cosine_precision, cosine_recall, cosine_ap, cosine_mcc
model-index: name: SentenceTransformer based on google-bert/bert-base-uncased
results: task: type: binary-classification
name: Binary Classification
dataset: name: Unknown
type: unknown
metrics: type: cosine_accuracy
value: 0.7932
name: Cosine Accuracy
verified: no, type: cosine_accuracy_threshold
value: 0.8014038801193237
name: Cosine Accuracy Threshold
verified: no, type: cosine_f1
value: 0.6446930752948291
name: Cosine F1
verified: no, type: cosine_f1_threshold
value: 0.7684383392333984
name: Cosine F1 Threshold
verified: no, type: cosine_precision
value: 0.641395908543923
name: Cosine Precision
verified: no, type: cosine_recall
value: 0.6480243161094225
name: Cosine Recall
verified: no, type: cosine_ap
value: 0.7217211669517005
name: Cosine Ap
verified: no, type: cosine_mcc
value: 0.46915729299516395
name: Cosine Mcc
verified: no
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