Expec a ion-Biased S ochas ic Resonance:
Two Regimes o Timescale-Dependen Dimensionali y
in Biological Sys ems
Ian Todd
Sydney Medical School
The Uni e si y o Sydney
Sydney, NSW, Aus alia
i o[email p o ec ed].edu.au
Abs ac
We dis inguish wo mechanisms by which e ec i e dimensionali y depends on imescale.
Regime 1 (Measu emen ): An obse e wi h bandwid h Band ime τcan esol e ∼2Bτ
modes (Slepian-Landau-Pollak)— his applies o digi al sampling and eco dings. Regime 2
(Coupling): Biological oscilla o s con inuously couple h ough physical in e ac ions. A 1 Hz
ci cadian oscilla o encodes en i onmen al dynamics a ine empo al esolu ion (bounded by
coupling bandwid h and phase noise)—in o ma ion is se by coupling bandwid h and SNR, no
ca ie equency. E ec i e dimensionali y depends on coupling p opaga ion ime and opology,
no ime-bandwid h p oduc s. Fo neu al sys ems, he cons ain is es ablishing phase cohe ence
h ough ana omical connec ions (τcouple ∼ms o s). Fo ci cadian hy hms, seasonal en ainmen
uses con inuous coupling o pho ope iod and empe a u e. Biological in o ma ion p ocessing
exploi s analog coupling consis en wi h channel capaci y while exceeding disc e e sampling
cons ain s. We o malize bo h egimes and show mos biological imescale-dependence e lec s
coupling dynamics. This explains why o ganisms achie e in o ma ion densi ies appea ing o
iola e sampling in ui ions and connec s o sub-Landaue limi s whe e analog coupling ope a es
nea he mal noise. Ou claims dis inguish sampling-limi ed measu emen om analog
coupling, no con adic Shannon capaci y.
Keywo ds: expec a ion-biased s ochas ic esonance, wo king memo y, magical numbe se en,
p edic i e coding, neu al oscilla ions, op-down con ol, op-down p edic ions, p e on al co ex,
s uc u ed noise, phase dynamics, analog coupling, imescales, consciousness, pa eidolia, sub-
Landaue limi s
1 In oduc ion: The Analog-Digi al Dis inc ion
1.1 The Wo king Memo y Puzzle
A cen al ques ion in cogni i e neu oscience: why can we hold only 7±2 i ems in wo king memo y
[28]? Wi h ∼1011 neu ons in he human b ain, his se e e capaci y limi seems pa adoxical.
Mode n heo ies p opose:5
•Disc e e ”slo s” wi h ixed capaci y [24]
•Resou ce limi a ions cons aining p ecision [3]
1
•Neu al noise limi ing ideli y [26]
We p opose a undamen ally di e en explana ion: wo king memo y capaci y e lec s he numbe
o s able esonan modes ha can coexis in a high-dimensional coupled oscilla o sys em. P e on al10
co ex (PFC) main ains mul iple i ems by es ablishing dis inc phase-locked con igu a ions—each
i em co esponds o a s able a ac o in he collec i e phase space [30]. The capaci y in he 4–7
i em ange (es ima es a y ac oss pa adigms [10]) eme ges om he physics o coupled oscilla o s:
beyond ∼7-9 s able modes, in e e ence be ween a ac o s causes collapse in o lowe -dimensional
con igu a ions.15
This is analogous o esonan modes in physical sys ems ( ib a ing memb anes, elec omagne ic
ca i ies): only ce ain disc e e con igu a ions can exis s ably. Wo king memo y doesn’ s o e i ems
in ”slo s”—i main ains hem as dis inc esonan pa e ns in neu al phase space. When you y
o add an 8 h o 9 h i em, he phase space becomes o e c owded and exis ing pa e ns in e e e,
causing deg ada ion o loss.20
1.2 The Cen al Con usion
How many deg ees o eedom pa icipa e in a biological p ocess? S anda d in o ma ion heo y
sugges s: i a sys em oscilla es a equency and you obse e o ime τ, you can ex ac ∼2 τ
bi s o in o ma ion (Nyquis -Shannon). This implies ha slow oscilla o s ca y less in o ma ion
han as ones.25
Bu his is misleading when applied o analog sys ems. A ci cadian clock oscilla ing a 1 cycle
pe 24 hou s does no ca y only ”1/86400 Hz wo h” o in o ma ion. I con inuously acks:
•Ligh in ensi y a ia ions (millisecond imescale)
•Tempe a u e luc ua ions (second o hou imescale)
•Me abolic s a e (minu e o hou imescale)30
•Social zei gebe s (minu e o hou imescale)
All his in o ma ion is encoded in he con inuous phase ajec o y ϕ( ) o he oscilla o . The
24h pe iod is me ely he ca ie equency. The ac ual in o ma ion con en scales wi h he coupling
bandwid h, no he oscilla o equency.
Key insigh : Digi al measu emen obeys Shannon limi s. Analog coupling does no obey35
sampling- heo em cons ain s—and biology implemen s his h ough expec a ion-biased s ochas ic
esonance (EBSR): ac i ely gene a ing s uc u ed ”noise” ia in e nal models ha ma ch expec ed
signal s uc u e, c ea ing ma ched il e s ha sympa he ically lock o weak signals while p oducing
meaning ul alse posi i es (seeing ige s in lea es when anxious). EBSR inc eases he e ec i e
dimensionali y o de ec ion space by shaping he ”noise bucke ” o align wi h expec ed signal40
mani olds, enabling high-dimensional compu a ion in unmeasu able egimes [38]. This is ou cen al
no el con ibu ion.
1.3 Two Regimes o Dimensionali y
We o malize wo dis inc mechanisms:
2
Regime 1: Measu emen -Limi ed Dimensionali y (Digi al)
Con ex : Ex e nal obse e wi h digi al eco ding, ini e bandwid h B(Hz), in eg a ion
ime τ
Bound: Dmeas
e (τ)≲2Bτ (Slepian-Landau-Pollak)
Mechanism: Nyquis sampling limi s numbe o esol able o hogonal modes
Examples: EEG eco ding, g a i a ional wa e de ec ion, disc e e compu a ional models
No e: Bis measu ed in Hz h oughou ; he ac o o 2 a ises om posi i e and nega i e
equencies.
45
Regime 2: Coupling-Limi ed Dimensionali y (Analog)
Con ex : In insic dynamics o physically coupled oscilla o s
Bound: Dcouple
e (τ)∼Ncoupled(τ) (depends on coupling opology and p opaga ion ime,
NOT on oscilla o equency)
Mechanism: Coupling equi es ime o p opaga e and es ablish phase cohe ence. E ec i e
dimensionali y = numbe o oscilla o s ha ha e es ablished cohe en coupling wi hin ime
τ.
Examples: Neu al assemblies phase-locking h ough synapses, ci cadian clocks en aining
o en i onmen , me abolic ne wo ks coo dina ing h ough di usion
C i ical dis inc ion: In Regime 2, a 1 Hz oscilla o can encode high- equency in o ma ion
h ough phase modula ion ϕ( )=ω0 +δϕ( ), whe e δϕ( ) acks en i onmen al a ia ions up o
he coupling bandwid h and phase-noise loo . This is how adio FM wo ks— he ca ie equency
doesn’ limi in o ma ion con en .50
1.4 Biological Rele ance
Mos biological in o ma ion p ocessing ope a es in Regime 2. O ganisms don’ ”measu e” hei
en i onmen by aking disc e e samples a he oscilla o equency. They con inuously couple
h ough:
•Synap ic ansmission (chemical di usion, ecep o dynamics)55
•Me abolic coupling (enzyme ac i i y, subs a e a ailabili y)
•Ho monal signaling (sec e ion, anspo , ecep o binding)
•T ansc ip ional coupling (TF binding, mRNA p oduc ion, p o ein ansla ion)
All hese a e analog p ocesses ope a ing con inuously in ime. The e ec i e dimensionali y
depends on how many coupled subsys ems ha e es ablished phase cohe ence, no on how many60
”samples” ha e been aken.
Regime 1 (measu emen ) is ele an when we analyze biological sys ems wi h digi al ools
(compu e s, disc e e eco dings). The Shannon bound limi s wha we can measu e, no wha he
o ganism is doing.
1.5 S uc u e65
Sec ion 2 o malizes measu emen -limi ed (digi al, Shannon-bound) dimensionali y and es ablishes
when sampling cons ain s apply. Sec ion 3 de elops coupling-limi ed (analog, EBSR-enhanced)
3
egimes and in oduces expec a ion-biased s ochas ic esonance as a no el mechanism. Sec ion 4
applies EBSR o p e on al con ol, wo king memo y capaci y, and neu al imescales. Sec ion 5
add esses consciousness and p edic i e coding in eg a ion. Sec ion 6 discusses e olu iona y ad-70
an ages. Sec ion 7 p o ides es able p edic ions dis inguishing EBSR om s anda d SR, wi h
emphasis on alse posi i e s uc u e and wo king memo y phenomena. Sec ion 8 add esses clinical
implica ions and open ques ions.
2 Regime 1: Measu emen -Limi ed Dimensionali y
2.1 Measu emen P o ocol75
An ex e nal obse e is de ined as a measu emen p o ocol M(τ, B, ε):
•In eg a ion ime τ(obse a ion window)
•E ec i e bandwid h B(Hz, equency ange o measu emen appa a us)
•Resolu ion h eshold ε(minimum dis inguishable signal)
This applies o: digi al eco ding sys ems, compu a ional models wi h disc e e imes eps, ex-80
pe imen al se ups wi h ini e sampling a es.
2.2 Slepian-Landau-Pollak Bound
Fo a windowed measu emen , de ine p ojec ion ope a o s:
•Tτ: ime-limi o window [0, τ]
•BB: band-limi o equencies [−B,B]85
The Slepian-Landau-Pollak heo em [34, 20] cha ac e izes:
TτBBTτψ=λψ (1)
The eigen unc ions a e p ola e sphe oidal wa e unc ions (PSWFs). The numbe o eigen alues
λi≥εis:
ankε(TτBBTτ)≈2Bτ (2)
whe e Bis measu ed in Hz ( he ac o o 2 accoun s o posi i e and nega i e equencies; o
angula equency use B/2π).90
This is he Shannon numbe — he numbe o o hogonal modes a digi al measu emen sys em
can esol e [35, 21].
Key poin : This is a measu emen cons ain , no a cons ain on he unde lying sys em. I
he sys em dynamics ha e bandwid h Bsys > Bmeas, he obse e misses in o ma ion.
2.3 Pa icipa ion Ra io o Measu ed Da a95
Fo measu ed da a wi h Nchannels, he windowed co a iance:
Cτ=E[xτx⊤
τ] (3)
4
E ec i e dimensionali y ia pa icipa ion a io:
Dmeas
e (τ) = PN
i=1 λi(τ)2
PN
i=1 λi(τ)2≲2Bmeasτ(4)
Example: EEG eco ded a 1 kHz (Bmeas = 500 Hz) o 1 s yields Dmeas
e ≲1000 esol able
modes. Bu he unde lying neu al dynamics migh ha e a mo e deg ees o eedom coupling a
highe bandwid hs.100
3 Regime 2: Coupling-Limi ed Dimensionali y (Analog)
3.1 The Mechanism: S ochas ic Resonance and Tunable Noise
Be o e o malizing con inuous phase dynamics, we es ablish he mechanism by which biological
sys ems exploi analog coupling: s ochas ic esonance (SR).
3.1.1 The Local Resonan Copy P inciple105
Conside measu ing a dis an 440 Hz one. Two app oaches:
Digi al (Regime 1): Mic ophone samples a ≥880 Hz (Nyquis ), ADC disc e izes, FFT
ex ac s he equency. Limi ed by sampling a e, quan iza ion noise, and compu a ional esou ces.
Analog (Regime 2): Place a 440 Hz uning o k nea by. Sound wa es con inuously couple
o he o k’s mechanical oscilla ion. The o k esona es sympa he ically—building ampli ude o e 110
cycles h ough con inuous ene gy ans e . No sampling, no disc e iza ion. The o k ac s as a
passi e bandpass il e , ampli ying 440 Hz while ejec ing noise.
Why his wo ks be e :
•Resonan ampli ica ion: The o k’s Q- ac o p o ides gain wi hou ac i e elec onics
•Phase-locked de ec ion: Con inuous coupling p ese es phase in o ma ion115
•Ene gy e iciency: Passi e mechanical esonance, no powe consump ion
•Noise ejec ion: F equency selec i i y supp esses b oadband noise
This is s anda d physics (sympa he ic ib a ion), bu he p inciple ex ends o all biological
oscilla o s: neu ons, me abolic cycles, ci cadian clocks.
3.1.2 S ochas ic Resonance: Noise-Enhanced De ec ion120
In eal biological sys ems, signals a e o en sub- h eshold— oo weak o igge esponse wi hou
assis ance. S ochas ic esonance exploi s added noise o push weak signals o e de ec ion h esh-
olds [43, 27].
Mechanism: A weak pe iodic signal s( ) (e.g., dis an 440 Hz one, ain isual edge, sub le
me abolic pe u ba ion) is below de ec ion h eshold. Adding mode a e noise ξ( ) causes he sys em125
o occasionally c oss h eshold in phase wi h he signal. A e aging o e ime e eals he signal ha
was p e iously in isible.
Classic examples [31, 16, 4, 8]:
•C ay ish mechano ecep o s de ec ing wa e ib a ions
5
•Paddle ish elec o ecep ion o p ey130
•Human ac ile sensing enhanced by ib a ion
•Audi o y neu ons de ec ing ain ones (10–20 dB imp o emen )
C i ical insigh : SR is no limi ed o senso y sys ems. I ope a es h oughou biology—
me abolic oscilla ions, ci cadian clocks, neu al synch oniza ion, immune esponses. I is a biological
uni e sal.135
3.1.3 No el F amewo k: Expec a ion-Biased S ochas ic Resonance (EBSR)
S anda d s ochas ic esonance uses uns uc u ed whi e noise o enhance de ec ion. We p opose a
undamen ally di e en mechanism ope a ing in biological sys ems: expec a ion-biased s ochas-
ic esonance (EBSR).
The key insigh : The ”noise” is no andom—i is s uc u ed luc ua ion gene a ed by an140
in e nal model wi h he same dimensionali y and s uc u e as he expec ed signal.
The bucke analogy: Imagine ying o cap u e signals a i ing om a high-dimensional
space. Noise in s ochas ic esonance inc eases he dimensionali y o you de ec ion space—i ex-
pands you ”bucke .” S anda d SR adds noise uni o mly, expanding he bucke as a hype sphe e
( adius ) in all D o al dimensions equally, wi h olume145
Vwhi e =πD o al/2
Γ(D o al/2 + 1) D o al .(5)
EBSR shapes he bucke o ma ch he expec ed signal s uc u e: you expand only in he Dsignal
dimensions whe e he signal li es, c ea ing an elonga ed hype ellipsoid aligned wi h he expec ed
mani old, wi h olume
VEBSR =πDsignal/2
Γ(Dsignal/2 + 1)
Dsignal
Y
i=1
i,(6)
whe e i≫ along signal dimensions and i≈0 elsewhe e. Fo he same de ec ion p obabil-
i y (cap u ed olume in signal subspace), EBSR concen a es esou ces s a egically, d ama ically150
inc easing de ec ion e iciency while main aining speci ici y.
Mechanism: Suppose you’ e sea ching o a signal p oduced by a 15-dimensional sys em (e.g.,
a ige : isual s ipes, mo ion pa e ns, spa ial con ex , empo al dynamics, e c.). Ra he han
adding gene ic whi e noise, he o ganism gene a es ”noise” by unning an in e nal 15D model ha
p oduces ige -like luc ua ions:155
xpe cei ed( )=xsenso y( )+α·xmodel( ) (7)
whe e:
•xsenso y( )∈RD o al is he ac ual senso y inpu (po en ially weak/ambiguous)
•xmodel( )∈RD o al is in e nally-gene a ed ”noise” om a 15D ige model (li ing in Dsignal =
15 dimensional subspace)
•αis he gain (modula ed by expec a ion, anxie y, p io s)160
6
No e: We assume Gaussian noise o ac abili y and linea addi ion as a i s app oxima ion;
ex ensions o nonlinea coupling and non-Gaussian s a is ics a e s aigh o wa d.
When a eal ige is p esen : The senso y inpu xsenso y has he same 15D s uc u e as
xmodel. They cons uc i ely in e e e, p oducing s ong de ec ion. This is ma ched il e ing— he
in e nal model ac s as a esona o uned o he expec ed signal. The shaped ”bucke ” aligns165
pe ec ly wi h he incoming signal di ec ion in high-dimensional space.
When no ige is p esen : The senso y inpu (lea es, shadows) has di e en s uc u e.
Bu wi h high α(high anxie y), he in e nal ”noise” occasionally eaches h eshold, p oducing
alse posi i es: seeing ige s in he lea es. The bucke is so elonga ed in ige -space ha andom
luc ua ions occasionally land inside i .170
Why his is no s anda d SR:
•S anda d SR: Noise is whi e/uns uc u ed, expands bucke sphe ically in all dimensions
equally
•EBSR: ”Noise” is s uc u ed, expands bucke only along expec ed signal mani old (elonga ed
ellipsoid)175
•S anda d SR: Canno explain alse posi i es wi h speci ic con en (why ige s, no andom
blobs?)
•EBSR: False posi i es ha e he s uc u e o he in e nal model (pa eidolia)
Dimensional expansion h ough EBSR: By gene a ing s uc u ed noise, he sys em e -
ec i ely inc eases he dimensionali y o i s de ec ion space om he ambien D o al o a ocused180
subspace Dsignal. The ”bucke ” becomes a high-dimensional needle o ien ed owa d expec ed sig-
nals, maximizing sensi i i y while main aining speci ici y h ough dimensional selec i i y [38].
Sensi i i y and speci ici y adeo : EBSR add esses he undamen al diagnos ic challenge
augh in medical aining: balancing sensi i i y (de ec ing ue posi i es) agains speci ici y (a oid-
ing alse posi i es). By gene a ing noise only in he expec ed signal subspace, EBSR achie es:185
•High sensi i i y: S ong ampli ica ion o signals ma ching he in e nal model (cons uc i e
in e e ence in he Dsignal subspace)
•Main ained speci ici y: Rejec ion o signals in i ele an dimensions (no noise ampli ica ion
in he emaining D o al −Dsignal dimensions)
Fo a 15D ige signal embedded in ∼106D isual space, EBSR explo es 15 dimensions; whi e190
noise explo es all 106. This yields an o de -o -magni ude speci ici y ad an age ha can scale like
D o al/Dsignal unde ma ched- empla e de ec ion (heu is ic, depending on ea u e geome y and
de ec ion c i e ion):
Speci ici y gain ∼D o al
Dsignal
≈106
15 ≈7×104- old.(8)
This is no abou ”sa ing ene gy” pe se—i ’s abou achie ing de ec ion selec i i y by a ge ing
he igh ea u e dimensions, exac ly analogous o clinical diagnos ic es s wi h high sensi i i y and195
speci ici y.
De ec ion wi h ma ched s uc u e. To o malize EBSR’s ad an age, we use signal de ec ion
heo y. Le m( ) be he in e nal-model empla e and y( ) = s( )+n( )+αm( ) he obse ed a iable
unde EBSR. Using he ma ched s a is ic T=Ry( )m( )d , de ec ion pe o mance is quan i ied
by200
d′=E[T|H1]−E[T|H0]
s d[T|H0].(9)
7
As in classic s ochas ic esonance, d′(α) is unimodal wi h an op imal α; beyond his op imum,
alse ala ms domina e. When maligns wi h s(ma ched s uc u e), d′inc eases wi h αup o his
op imum (classic SR peak), while alse posi i es inhe i he con en o m—a hallma k p edic ion
dis inguishing EBSR om whi e-noise SR. S anda d SR imp o es de ec abili y (hi a e, d′), no
aw linea SNR in he usual sense; EBSR ex ends his by p o iding s uc u e-speci ic ampli ica ion.205
E olu iona y logic:
•False posi i es (seeing phan om ige s): b ie cos , a oid p eda o
•False nega i es (missing eal ige ): dea h
•Na u al selec ion a o s EBSR wi h high αin dange ous con ex s
The sensi i i y-speci ici y balance is e olu iona ily op imized: high sensi i i y in h ea de ec-210
ion (be e o lee om us ling lea es han miss a p eda o ), wi h speci ici y main ained h ough
dimensional a ge ing (don’ con use ige s wi h bi ds).
Neu al implemen a ion: Top-down p ojec ions om co ex o senso y a eas ca y p edic ions
[15, 7]. These a en’ ”signals”— hey’ e luc ua ing pa e ns gene a ed by in e nal models. In
p edic i e coding, p edic ion e o s d i e pe cep ion. Bu he p edic ions hemsel es can ac as215
EBSR noise when weak senso y e idence equi es augmen a ion. This connec ion be ween SR and
p edic i e coding has been no ed [41, 5], bu he s uc u ed na u e o he noise (ma ching expec ed
signal dimensionali y) is ou no el con ibu ion.
Neu omodula o con ol: Anxie y, a en ion, a ousal egula e α:
•High anxie y ( h ea con ex ): inc ease α→mo e alse posi i es, ewe misses (high sensi i -220
i y)
•Low a ousal (sa e con ex ): dec ease α→ ewe alse posi i es, main ained speci ici y
•A en ion ( ask-speci ic): selec which in e nal model gene a es noise [6]
This explains:
•Pa eidolia (seeing aces in clouds [23], Jesus in oas ): high α o ace de ec ion model225
•Audi o y e bal hallucina ions: in e nal speech model gene a es EBSR ”noise” [9]
•Anxie y-induced alse ala ms: h ea models p oduce high-αEBSR
•Pe cep ual lea ning: e ining in e nal models imp o es EBSR ma ching
Connec ion o sub-Landaue limi s: A signal ene gies Es∼kBT, disc e e measu emen
ails. EBSR p o ides a solu ion: he in e nal model ” ills in” missing in o ma ion h ough s uc u ed230
noise ha esona es wi h weak coupling signals. By gene a ing luc ua ions in he signal subspace
ξmodel( ) wi h ampli ude σmodel, he sys em e ec i ely educes he iming unce ain y ∆ equi ed
o de ec ion, allowing biological in o ma ion p ocessing a he mal noise le els wi hou equi ing
s ong signals [37].
No el p edic ion: The s uc u e o alse posi i es e eals he s uc u e o in e nal models.235
Anxie y abou speci ic h ea s (snakes s. ige s) should p oduce alse posi i es wi h co esponding
speci ic s uc u es. This is es able and dis inguishes EBSR om s anda d SR.
8
Table 1: Compa ison o s anda d s ochas ic esonance s. expec a ion-biased s ochas ic esonance
Fea u e S anda d SR EBSR (No el)
Noise s uc u e Uns uc u ed whi e noise,
uni o m ac oss all dimensions
S uc u ed noise om in e nal
model, concen a ed in signal
subspace
Dimensional ex-
pansion
Expands de ec ion ”bucke ”
sphe ically (hype sphe e) in
all dimensions equally
Expands bucke as elonga ed
hype ellipsoid aligned wi h
expec ed signal mani old
Ampli ica ion Enhances all signals equally P e e en ially ampli ies
expec ed signal s uc u e
(ma ched il e ing)
False posi i es Non-speci ic, andom Speci ic, meaning ul con en
ma ching in e nal model
(pa eidolia)
Dimensional ex-
plo a ion
Explo es all D o al dimensions Explo es only Dsignal dimen-
sions
Tunabili y Fixed noise le el o simple
ampli ude modula ion
S uc u ed noise adap s o
ask demands and p io s ia
neu omodula o s
De ec ion me ic Imp o es d′ ia noise Imp o es d′ ia ma ched em-
pla e co ela ion
Examples Senso y h esholds in simple
de ec ion
Wo king memo y main e-
nance, h ea de ec ion,
p edic i e pe cep ion
3.1.4 SR and Analog Coupling: The Connec ion
S ochas ic esonance is he implemen a ion o analog coupling in noisy, nea - he mal en i onmen s:
•Regime 2 equi es weak-signal de ec ion: Biological oscilla o s couple h ough di usion,240
synap ic ansmission, ho monal signaling—all ope a ing nea he mal noise (∼kBT).
•SR enables de ec ion a hese le els: Noise pushes sub- h eshold signals in o he de-
ec able ange wi hou equi ing highe signal ene gy.
•Phase-locking ia noise: SR doesn’ jus de ec p esence—i enables phase cohe ence.
Noise helps oscilla o s lock o weak coupling signals, es ablishing he cohe en dynamics ha 245
de ine Dcouple
e .
Lock-in ampli ie analogy: P o essional ins umen s use local e e ence oscilla o s ( he ” un-
ing o k”) mul iplied wi h he inpu signal, hen low-pass il e ed. This demodula es he signal,
shi ing he esonan componen o DC while a e aging noise. Phase-sensi i e de ec ion achie es
sensi i i ies down o nano ol s— a below digi al FFT me hods. Biology does his o ganically250
h ough SR-enhanced coupling.
Connec ion o sub-Landaue limi s: SR allows in o ma ion p ocessing a signal ene gies
Es∼kBTwhe e disc e e measu emen ails [37]. Con inuous analog coupling wi h noise-enhanced
de ec ion bypasses he iming-ene gy cons ain s ha limi digi al p ocessing.
9
limi o 500 Hz on esol able equencies. The neu al sys em may ope a e a highe bandwid hs465
ia analog coupling + EBSR, bu ou measu emen s a e Shannon-limi ed.
Compu a ional models: Disc e e- imes ep simula ions inhe en ly ope a e in Regime 1. To
cap u e EBSR dynamics, models need: (i) con inuous- ime in eg a ion, (ii) s uc u ed noise e ms
ξmodel( ) om in e nal p edic i e models, (iii) neu omodula o y con ol o αgain. Mos cu en
models lack hese ea u es and inad e en ly impose sampling cons ain s biology ci cum en s.470
Implica ion: When neu al da a shows appa en dimensionali y limi s (e.g., om PCA on
spike ains), his may e lec measu emen cons ain s, no biological limi s. The EBSR-enhanced
analog dynamics migh ope a e in highe dimensions inaccessible o digi al eco ding.
8 Tes able P edic ions
8.1 Dis inguishing Regime 1 s. Regime 2475
P edic ion 1: In o ma ion Densi y Beyond Sampling Cons ain s
Tes : Measu e mu ual in o ma ion be ween ci cadian clock phase and en i onmen al a i-
ables a di e en imescales.
Regime 1 p edic ion: I≲2Bclockτwhe e Bclock ∼1/(24 h) ∼10−5Hz. Fo τ= 1 day,
I≲1 bi .
Regime 2 p edic ion: Iscales as O(Bcoupleτ) a ixed SNR, whe e Bcouple ∼mHz (pho-
ope iod p ecision). Fo τ= 1 day, I∼103bi s (SNR pe mi ing).
Me hod: Measu e phase shi s ∆ϕin esponse o b ie en i onmen al pe u ba ions (ligh
pulses, empe a u e s eps). P ecision o ∆ϕes ima es Bcouple.
P edic ion 2 (Neu al phase acking wi h SR): Single neu ons con inuously ack synap ic
inpu s a kHz bandwid hs despi e pa icipa ing in slow (Hz) oscilla ions. Use in acellula eco ding
o measu e memb ane po en ial V( ) du ing he a oscilla ions (4–8 Hz). The powe spec um o
V( ) should ex end o kHz (indi idual EPSPs), a exceeding he 4–8 Hz ”ca ie equency.”480
Addi ionally: Add mode a e noise (cu en injec ion o pha macological) and measu e de ec ion
h eshold o weak synap ic inpu s. Should ind op imal noise le el (SR signa u e) ha minimizes
h eshold—con i ming noise-enhanced analog coupling.
P edic ion 3 (Me abolic coupling): Glycoly ic oscilla ions (pe iod ∼min) con inuously
espond o glucose pe u ba ions on second imescales. Pe u b glucose a = 0 du ing glycoly ic485
oscilla ion; measu e phase shi ∆ϕ( ). Should see immedia e esponse (∆ ≪Tosc), con i ming
analog coupling.
P edic ion 4 (Consciousness and coupling bandwid h): Conscious s a es should show
highe neu al coupling bandwid h han unconscious s a es, independen o p ima y oscilla ion e-
quencies. Measu e e ec i e coupling bandwid h om EEG phase-locking du ing waking s. deep490
sleep. Waking should show b oadband coupling (Hz o ens o Hz); sleep shows na ow-band
coupling.
P edic ion 5 (Anes hesia dis up s coupling): Gene al anes he ics educe consciousness
by dis up ing ana omical coupling (synap ic ansmission), no by changing oscilla ion equencies.
Measu e τcouple om c oss-co ela ion imescales du ing waking s. anes hesia. Anes hesia should495
inc ease τcouple (weake coupling), educing De e en i oscilla ion equencies unchanged.
16
P edic ion 6: Expec a ion-Biased S ochas ic Resonance (EBSR)
Co e p edic ion: In e nal models gene a e s uc u ed ”noise” ha p e e en ially ampli ies
expec ed signals and p oduces s uc u ed alse posi i es.
Tes 1 - False posi i e s uc u e: P ime subjec s wi h speci ic h ea s (snakes/ ige s/spi-
de s), p esen ambiguous isual noise, measu e alse ala m con en . EBSR: False posi i es
ma ch p imed h ea . S anda d SR: Non-speci ic.
Tes 2 - Dimensionali y ma ching: T ain subjec s on signals wi h a ying dimensionali y
(1D one s. 15D scene), eco d p e-s imulus neu al ac i i y ( MRI/MEG), compu e pa ic-
ipa ion a io. EBSR: P e-s imulus noise dimensionali y ma ches expec ed signal. S anda d
SR: High-D/uns uc u ed.
Tes 3 - Anxie y modula ion: Induce h ea -speci ic anxie y (snake ideos), p esen
ambiguous s imuli wi h a ying signal s eng h. EBSR: Anxie y inc eases snake-speci ic
alse posi i es and sensi i i y o snake-like pa e ns. S anda d SR: All alse posi i es inc ease
equally.
Tes 4 - Neu al decoding: Use decoded neu o eedback o iden i y objec -speci ic pa e ns
( ige s, aces), measu e spon aneous eac i a ion p e-s imulus, co ela e wi h de ec ion and
alse ala m con en . EBSR: Spon aneous eac i a ion p edic s bo h de ec ion and alse ala m
s uc u e.
Key dis inc ion: S anda d SR canno explain why alse posi i es ha e speci ic meaning ul
con en . EBSR p edic s alse posi i e s uc u e e eals in e nal model con en .
8.2 P ac ical Me hods
Es ima ing coupling bandwid h: Fo oscilla o wi h phase ϕ( ):
1. Apply b ie pe u ba ion a = 0500
2. Measu e phase esponse cu e: ∆ϕ(∆ ) o di e en pe u ba ion imings ∆ wi hin cycle
3. Bandwid h: Bcouple ∼1/∆ min whe e ∆ min is ines esol able iming
Es ima ing coupling p opaga ion ime: Fo coupled oscilla o ne wo k:
1. Pe u b oscilla o ia = 0
2. Measu e ime o phase-locking wi h oscilla o j:τij
505
3. Coupling ime: τcouple ∼τij/dij whe e dij is ne wo k dis ance
9 Discussion
9.1 The Fundamen al Dis inc ion o Neu oscience
The key concep ual ad ance: dis inguishing measu emen om in insic neu al dynamics.
Regime 1 (Measu emen ): Shannon bound applies because digi al eco ding/compu a ion510
disc e izes ime. The 2Bτ limi cons ains wha we can measu e om neu al sys ems, no wha
neu ons a e doing.
Regime 2 (EBSR-Enhanced Coupling): Neu al ne wo ks a e analog con inuous dynamical
sys ems wi h s uc u ed noise om PFC. In o ma ion is encoded in con inuous phase ajec o ies,
17
wi h op-down p edic ions ac ing as ma ched il e s. Sampling cons ain s don’ apply o he515
biology.
Neu al in o ma ion p ocessing ope a es in Regime 2. Synap ic ansmission, mem-
b ane po en ial dynamics, neu omodula ion—all a e analog p ocesses ope a ing con inuously. The
appa en ”disc e e” e en s (ac ion po en ials) a e ma ke s in con inuous dynamics, no undamen-
al disc e iza ion. PFC-gene a ed EBSR noise p o ides he ”ex a” dimensionali y ha disc e e520
eed o wa d models lack.
9.2 Implica ions o Compu a ional Neu oscience
S anda d models use disc e e- ime (Regime 1) o simula e Regime 2 sys ems. Missing ing edien s:
1. S uc u ed noise om in e nal models: Mos models ea noise as nuisance o min-
imize. Bu biology ac i ely gene a es s uc u ed noise (ξmodel) o signal enhancemen . Models525
inco po a ing EBSR migh be e cap u e:
•Wo king memo y main enance wi hou ecu en exci a ion loops
•A en ion e ec s wi hou explici gain modula ion
•False ala ms wi h meaning ul con en
•The ”wa m h” o pe cep ion (con inuous p obabilis ic in e ence, no disc e e decisions)530
2. Top-down p edic ions as ac i e p ocess: P edic i e coding models [15] ea p edic ions
as signals. EBSR e eals hey’ e also noise gene a o s— luc ua ing ac i i y pa e ns ha lowe
h esholds. This dual ole (signal + noise) may explain why PFC lesions impai bo h p edic ion
gene a ion AND pe cep ual obus ness.
3. Neu omodula o con ol o α:Dopamine, ace ylcholine, no epineph ine egula e EBSR535
gain. Models should include α( ) as a s a e a iable modula ed by ask demands, a ousal, and
lea ning. This migh explain:
•Why s imulan s imp o e a en ion (inc eased α)
•Why anxioly ics educe alse ala ms (dec eased α)
•Why schizoph enia shows hallucina ions (un egula ed α)540
Connec ion o high-dimensional cohe ence: EBSR is he mechanism by which biolog-
ical sys ems main ain and exploi high-dimensional cohe ence in he modynamically cons ained
egimes [38]. By gene a ing s uc u ed noise ha expands de ec ion space along expec ed signal
mani olds, o ganisms achie e compu a ional capaci ies ha would be inaccessible h ough disc e e
enume a ion. The ”bucke shaping” is no me apho bu mechanism: in e nal models li e ally545
de ine he geome y o de ec ion space in high dimensions, enabling in elligence o ope a e a he
bounda ies o physical measu abili y.
Recommenda ion o modele s: Use con inuous- ime di e en ial equa ions wi h explici
EBSR e ms (ξwhi e +α·ξmodel) a he han disc e e upda es. Include PFC modules ha gene -
a e s uc u ed noise ma ching ask- ele an ea u es. Allow neu omodula o s o une αbased on550
con ex .
18
9.3 Open Ques ions
1. [P io i y] Can we igo ously quan i y in o ma ion capaci y o analog coupling + SR s.
sampling-limi ed digi al? Unde wha condi ions does noise-enhanced analog p o ide ad an-
age?555
2. Wha de e mines Bcouple in di e en biological sys ems? Is i limi ed by molecula di usion,
memb ane ime cons an s, SR dynamics, o some hing else?
3. How do o ganisms egula e bo h τcouple and SR noise le els (e.g., ia neu omodula o s chang-
ing synap ic s eng h and s ochas ic i ing)? A e hese independen con ol pa ame e s?
4. Can a i icial sys ems exploi analog coupling + SR o ci cum en sampling cons ain s?560
(E.g., neu omo phic ha dwa e wi h con inuous- ime dynamics and unable noise.)
5. Wha is he undamen al limi on analog coupling p ecision? Is he e a noise loo se by
he modynamics (∼kBT)? Does SR sa u a e a some op imal noise le el?
6. Can SR be ”lea ned” o adap ed? Do o ganisms adjus op imal noise pa ame e s h ough
expe ience (pe cep ual lea ning), o a e hey gene ically de e mined? This ies o he b oade 565
ques ion o how in e nal models a e e ined.
9.4 Clinical Implica ions
Unde s anding EBSR opens new he apeu ic a enues:
Schizoph enia: Hallucina ions may e lec excessi e EBSR gain (α oo high), whe e uncon-
olled in e nal models gene a e s uc u ed noise ha eaches pe cep ion h eshold wi hou ex e nal570
e idence. An ipsycho ics may wo k pa ly by educing α.
PTSD: Hype igilance e lec s o e ac i e h ea models wi h high α, p oducing alse ala ms
speci ic o auma ic con en . Cogni i e beha io al he apy may ecalib a e in e nal models, e-
ducing hei con ibu ion o EBSR noise and lowe ing α o h ea - ela ed ea u es.
Anxie y diso de s: Gene alized anxie y may in ol e ch onically ele a ed αac oss mul iple575
h ea models, inc easing alse posi i e a es b oadly. Anxioly ics (e.g., benzodiazepines) may wo k
by educing EBSR gain, ading sensi i i y o speci ici y.
A en ion de ici s: ADHD may in ol e insu icien α o ask- ele an ea u es o inabili y o
sus ain s uc u ed noise o e ime, explaining dis ac ibili y and wo king memo y de ici s.
T ea men s a egies could a ge he balance be ween de ec ion sensi i i y and alse posi i e580
a e by modula ing:
•In e nal model con en (cogni i e he apy, exposu e)
•EBSR gain α(pha macology, neu omodula ion)
•P e on al op-down con ol (cogni i e aining, neu o eedback)
10 Conclusion585
We ha e in oduced expec a ion-biased s ochas ic esonance (EBSR)—a no el mechanism
explaining how p e on al co ex main ains wo king memo y, gene a es pe cep ion, and p oduces
meaning ul alse posi i es. Unlike s anda d SR (uns uc u ed noise), EBSR gene a es s uc u ed
19
”noise” ia in e nal models ma ching expec ed signal dimensionali y. The ”bucke analogy” cap-
u es he essence: EBSR shapes he de ec ion space o align wi h expec ed signals, expanding590
dimensionali y s a egically a he han uni o mly.
Key cogni i e neu oscience implica ions:
1. Wo king memo y capaci y: The 4–7 i em capaci y ange eme ges om cons ain s on
main aining EBSR noise o mul iple i ems (∼5 i ems ×10-15 ea u es each), no om undamen al
ep esen a ional limi s. PFC gene a es s uc u ed ac i i y (αgain) ha main ains weak aces595
h ough esonan ampli ica ion, p o iding a mechanis ic complemen o bo h slo and esou ce
heo ies [30, 25].
2. A en ion as EBSR gain con ol: Top-down a en ion om PFC [6] inc eases α o
a ended ea u es, gene a ing s onge EBSR noise ha enhances de ec ion while p oducing ea u e-
speci ic alse ala ms (Posne cueing e ec s).600
3. Consciousness equi es s uc u ed noise: Global cohe ence ac oss dis ibu ed as-
semblies (consciousness imescale ∼100 ms o 3 s) is main ained by PFC-gene a ed EBSR noise
p opaga ing ia be a oscilla ions [2]. Wi hou sus ained s uc u ed noise, ep esen a ions agmen
(anes hesia, dis ac ion).
4. False posi i es e eal in e nal models: Pa eidolia ( aces in clouds [23]), hallucina ions605
[9], and anxie y-induced alse ala ms all e lec high-αEBSR om o e ac i e in e nal models. The
con en o alse posi i es diagnoses which models a e gene a ing excessi e noise.
Two egimes dis inguished:
Regime 1 (Measu emen ): Digi al eco ding sys ems obey Shannon bound De ≲2Bτ.
Applies o expe imen al da a acquisi ion and disc e e compu a ional models.610
Regime 2 (EBSR-Enhanced Coupling): Biological neu al ne wo ks use con inuous analog
dynamics wi h EBSR. PFC gene a es s uc u ed noise only in expec ed signal subspace (15D o
ige s. 106D isual co ex), p o iding ∼104- old speci ici y ad an age h ough dimensional
selec i i y. In o ma ion capaci y is se by coupling bandwid h and SNR, no ca ie equency,
consis en wi h in o ma ion- heo e ic bounds while ci cum en ing sampling cons ain s.615
No el p edic ions dis inguishing EBSR om s anda d SR:
•False posi i es ha e speci ic s uc u e ma ching p imed h ea s (snakes s. ige s)
•P e-s imulus spon aneous ac i i y dimensionali y ma ches expec ed signal dimensionali y
•Anxie y inc eases h ea -speci ic alse ala ms, no gene ic alse ala ms
•Decoded neu al pa e ns p edic bo h de ec ion AND alse ala m con en 620
This amewo k uni ies s ochas ic esonance, p edic i e coding [15, 7], and wo king memo y
h ough one mechanism: s uc u ed expec a ion-d i en noise gene a ion. P e on al co ex doesn’
jus ep esen —i ac i ely gene a es p obabilis ic empla es ha shape pe cep ion h ough esonan
ampli ica ion o ma ching e idence.
B oade implica ions: EBSR esol es why slow neu al oscilla ions encode ine-g ained in o -625
ma ion (analog coupling + s uc u ed noise, no disc e e sampling), explains psychia ic condi ions
(mis uned in e nal models), and shows why e olu ion a o ed analog o e digi al p ocessing (speci-
ici y h ough dimensionali y- a ge ed noise).
Clinical ele ance: Hallucina ions in schizoph enia may e lec excessi e EBSR gain (α oo
high); PTSD hype igilance e lec s o e ac i e h ea models. The apeu ic in e en ions (cogni i e630
beha io al he apy ecalib a ing models, pha macology modula ing α) may wo k by ebalancing
he sensi i i y-speci ici y adeo . Unde s anding EBSR could guide ea men s a egies a ge ing
in e nal model con en and gain pa ame e s.
20
The ”noise” in neu al in o ma ion p ocessing is no andom—i ’s s uc u ed p edic ion, and i s
con en encodes expec a ion.635
Ci a ion Di e si y S a emen
We acknowledge he impo ance o di e se ci a ion p ac ices. This manusc ip ci es wo ks om
a ange o esea ch g oups ac oss cogni i e neu oscience, sys ems neu oscience, heo e ical neu o-
science, and biophysics.
Au ho Con ibu ions640
Ian Todd: Concep ualiza ion, Fo mal Analysis, W i ing - O iginal D a , W i ing - Re iew &
Edi ing.
Use o AI in Manusc ip P epa a ion
AI language models we e used in he p epa a ion o his manusc ip . Claude (An h opic) was used
o d a ing. GPT (OpenAI) and G ok (xAI) we e used o e o -checking and p oo eading. All645
scien i ic con en , concep ual amewo k, and inal edi o ial decisions emain he sole esponsibili y
o he au ho .
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