tamaso mā jyotirgamaya: Seeking the Self Amidst Covids ... · R.x. Covea & B. Mishra tamaso ma jyotirgamaya: Seeking the Self¯ A minuscule subset of the visible physical world is

tamaso ma jyotirgamaya: Seeking the Self AmidstCovids’ Cytokine CyclonesR.x. Covea and B. (Bud) Mishra, Math & CS, Courant In-stitute of Mathematical Sciences; CSE, Tandon School of En-gineering; Cell Biology, NYU School of Medicine; QB, ColdSpring Harbor Lab; Oncology, New York Genome Center;Hum. Genetics, Mt. Sinai School of Medicine; Covid-19 Re-searcher, RxCovea, etc. New York, USA

15 August 2020

Pondering on pandemics and the promise of purification

from the plethora of problems that it has spawned, the

paper builds on a game theoretic model of host-pathogen

interaction, and... moves beyond. It highlights how quicklythis ‘wicked’ problem has led to deceptive Nash equilibria of certaininformation-asymmetric games as well as their sequels of more com-plex intertwined games at human scale but without an exit strategy insight. In the absence of clarity (e.g., access to complete information)and yet facing a capricious and complex conspirator, we overview anexemplary solution, created by RxCovea, and examine how it mighthelp.

A Rival Viral Arrival

Figure 1: Molecules, Molecular Patternsand (Pathogen/Danger) AssociatedMolecular Patterns: Who signals who?We depict the three worlds, importantto defining a host’s self and protectedby a complex immune system, butamenable to invasion by a simpledeceptive virus, which in turn can bedeceived by a vaccine. We develop asignaling game framework to studyvirology, and immunology — whilewe hope to extend the framework toasymptomatic patients, with misalignedutilities, and impaired by moral hazardsin economy. We suggest that they allconspire to make the Covid problema “wicked” (difficult or impossible tosolve) problem. Courtesy R.x. Covea etal.

All genesis stories might as well start with the picture

of the three worlds that we have borrowed from Sir

Roger Penrose. In our modified picture, the three worlds corre-spond to the physical world, symbolic world and signaling world,assembled in an ecosystem in which one devours the next and isdevoured by the one before. The picture probably had its origin inKabbalah, as depicted by Giordano Bruno as mundus triplex in hisbook De Magia. Bruno’s three worlds were: the archetypical world (ofdivine magic), the sensible world (of physical magic) and the rationalworld (of mathematical magic). During his lifetime, which over-lapped with Galileo’s, Bruno’s ideas, however, remained poorly un-derstood. In 1600, Bruno was burned at the stake in Rome’s Campode’ Fiori, after being tried for heresy by the Roman Inquisition. Likemany other contemporaneous Averroistas, Bruno was seeking deeperanswers: Which of these three worlds represent an objective (soundand complete) truth? And how can one separate truth from falsityto find ones’ true-selves – separate from non-selves? And would itconverge to a stable self-hood, albeit a conventional NE (Nash equi-librium)?

R.x. Covea & B. Mishra tamaso ma jyotirgamaya: Seeking the Self

A minuscule subset of the visible physical world is comprised ofmolecules, made out of atoms, and can be modeled mathematically us-ing tools from quantum and classical mechanics – but not necessarilyin a unified framework. Biomolecules constitute an important subclassof molecules and are dominated by phosphorous, carbon, nitrogen,oxygen, hydrogen, etc. The biomolecules interact with each other andwith water molecules (e.g., via ATP hydrolysis reaction process) It isimportant that the “cellulariziang” ensembles of such biomolecules– very likely membrane separated from the environment – remainlively (via a sequence of endergonic and exergonic reactions) and safe(maintaining right pH level and avoiding H2O2, etc.). Because liveli-ness and safety conferred to the cells can be abstracted by a “utility”function, cells may be abstracted as individual “biomolecular agents”competing with each other in an evolutionary game in which thefittest survives and replicates.

These biomolecules are also able to store useful information viaconcatenation of ATP-like sub-unit monomers to form polymers(e.g. RNA, DNA, microtubles, etc.) and thus, symbolically encodemolecular patterns, each with its own utility. Such polymers form thesymbolic world, in which they duplicate (or allow transcription andtranslation into other polymers mapping homomorphic patterns) andpropagate the information stored in molecular patterns. If the dupli-cation process permits variations and a utility-dependent replicatordynamics and pattern-specific information propagation is unidirec-tional, it sets the stage up for a Darwinian evolution and amplifiesdiversity, giving rise to inter-agent information asymmetry. Thus notall possible molecular patterns would be uniformly (or information-symmetrically) represented in the symbolic world; only an infinites-imally small subset of all possible patterns would encode viablegenomes (DNA), transcriptomes (RNA) or proteomes (proteins).

Immune System Glossary:The immune system is a host defense

system comprising many bio-molecularstructures and signaling processeswithin an organism that protectsagainst pathogens, dangerous (andpossibly, stranger) to the organism –from viruses to parasitic worms, anddistinguish them from the organism’sown healthy tissue. It is possible tostudy the immune systems as a sig-naling game whose Nash equilibriaseparate two types: Self and Non-self.The immune system consists of an In-nate system coupled with an Adaptivesystem: both following replicator dy-namics, but Innate system selecting overorganisms’ germ line and Adaptive sys-tem adapting over organisms’ somaticimmunological memory. [Adapted fromhttps://morgridge.org/outreach/]

Interactions among biological macro-molecules may be describedusing a sender-receiver signaling structure, where an expressedmacro-molecule such as a protein or RNA, constitutes a signal senton behalf of a sender agent (e.g., cell). The signal may be modeledas the three-dimensional conformation and physicochemical prop-erties of the macro-molecule. A receiver agent (e.g., another macro-molecule) may then bind to the signal macro-molecule, which pro-duces an action (such as an enzymatic reaction). The action producesutility for the participating agents, sender and receiver, and thereby– albeit indirectly – a change in overall fitness of the organism, andhence its genome (in evolutionary game theory, utility and fitnessare treated as analogous). When there is common interest, the utilityis expected to benefit both sender and receiver and their selectivity,thus driving Darwinian co-evolution. If there is neither common

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identity (i.e., they are “strangers”) nor common interest (i.e., theypose “dangers”), the sender and receiver may avoid each other inorder not to undermine their common fitness. Thus evolution of pro-cesses encoding, recognising and acting against PAMP (PathogenAssociated Molecular Patterns) and DAMP (Danger AssociatedMolecular Patterns) play an important role in the evolution of themulti-cellular immune systems. Note that not all strangers are dan-gerous (e.g., symbionts such as corona virus in bats) and that somenon-strangers could be dangerous (e.g., cytokine storms inducingactivated white blood cells).

But since the immune systems also play an important role in defin-ing many more higher order evolutionary processes: e.g., HLA diver-sity, mate-selection, cognitive processes, culture, etc., our very humanintellectual and cultural journey has also shaped our secular scientificunderstanding of the physical universe, albeit, it still remains incon-sistent and lacks unification (e.g., quantum and classical mechanics).The resulting body of scientific literature, however, forms only asmall part of our body of human knowledge that relates us to a ten-tative, though conventional, picture of a ‘natural world,’ containingboth symbolic and signaling systems.

As humans struggle with their understanding of the genesis andmitigation of a surging pandemic, initiated by a single zoonosis eventin a remote Asian town, it is worthwhile to meditate on these connec-tions among the three worlds – mundus triplex, further sub-dividedand re-connected by such sub-disciplines as virology, immunology,epidemiology, logical/mathematical inference and economics – goingfrom nano-scale viruses to global-scale human societies.

Or, “must we wring the neck of a certain system in order to stuffthem into [] pigeon holes for the satisfaction of the analogy mon-gers1:” Do the worlds divide neatly into Bruno’s three magics – sci- 1 Samuel Beckett. Dante ... Bruno, Vico

... Joyce. Our Exagmination Round HisFactification for Incamination of Work inProgress, 1929

ences into three disciplines: physics, mathematics and divine? Ordoes it just model a biological Gödelian self-referential self-seeking,selfishly greedy computation, hopelessly aspiring to halt with sta-ble (sound and complete) Turing decidability notion(s) of self(-ves)?Can it reach an NE (Nash equilibria), in which self separates fromnon-self, decoy epitopes from neutralizing, susceptible from infected,symptomatic from asymptomatic, essential economic activities fromdispensable?

Evolutionary Signaling Game

Replicator dynamics allow the signaling game to be couched in evo-lutionary terms 2. Replicator dynamics arise from the increased repli- 2 B. Skyrms. Signals. Oxford University

Press, Oxford, 2010cation of players with higher utility (fitness). Thus, if a cell has a

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strategy that results in increased utility, then it will increase in fre-quency in a population. For a sender cell this would entail sending asignal that may result in an increased utility, while for a receiver cellthis would entail undertaking an action that likewise may result in animproved utility (e.g., growth rate).

S

S

R

R

R

R

TC

TD

c

c

d

d

(1,1)*

(0,0)

(1,-1)

(0,0)

trust

reject

(0,0)

trust

reject

reject

reject(0,0)

Figure 2: Extensive Form SignalingGame, describing bio-mimicry by avirus to fool the immune system: Cellcan be of two types TC (self) or TD(non-self viral) : they can send c signalshonestly or by mimicry, respectivelyand may be trusted or rejected by theimmune system; similarly they cansend d signals erroneously or honestly,respectively and may be rejected by theimmune system. Courtesy S. Massey etal.

As already suggested, these dynamics represent a process anal-ogous to Darwinian (adaptive) evolution or positive selection. Inother words, as part of the innate immune system, sender agent, adendritic cell (DC), in a multicellular organism that recognizes anappropriate DAMP/PAMP combination could signal receiver agent,a macrophage (MΦ), to engulf and digest foreign substances (asso-ciated with the molecular patterns, AMP) in an action process calledphagocytosis. The innate system is said to be engaged in a signal-ing game, in which DC is the sender; MΦ, the receiver; they signalusing cytokines and phagosytosis is the action taken by the receiverupon receiving the signal. Their utility is determined by protectionthey confer against non-self (mostly danger, potentially posed bystrangers) and tolerance for self. Since, many pathogens (e.g., SARS-Cov-2) can engage in deception (e.g., entering a host cell by targetinghost ACE2 receptor – by binding to a site somewhat distant fromthe ACE2 canonical binding site), innate immune system may needother auxiliary adaptive agents to be “educated” ex tempore, repli-cate dynamically and retain memory. These cells belonging to theadaptive immune system are not strategic (e.g., do not confer fitnessalong the germ line) but play an important role as recommenders(B-cells) and verifiers (T-cells) in taming the deceptive pathogens thatcan grow and mutate rapidly to frustrate the innate immune system.However, in an adversarial chase, pathogens can evolve strategies tofrustrate the education of T-cells (e.g., antigen presentation), but canbe remedied by costly signaling via DC’s maturation and chemotaxisto germinal centers. It is no wonder, most immunology jokes endwith the punchline3, “The immunologist says, ‘The thing is, the im- 3 Ed Yong. Immunology is where

intuition goes to die. The Atlantic, 2020mune system is very complicated . . . ’ And the cardiologist says, ‘Justshoot me now.”

We hope to simplify the model by formulating the innate immunesystem as a signaling game 4 , which, though prone to deception, 4 B. Skyrms. Signals. Oxford University

Press, Oxford, 2010; and Simon M.Huttegger, Brian Skyrms, Rory Smead,and Kevin J. S. Zollman. Evolutionarydynamics of lewis signaling games:signaling systems vs. partial pooling.Synth., 172(1):177–191, 2010

can be critically tamed by the education, surveillance and memoryacquired by the adaptive immune system; the education of the adap-tive immune system, though highly costly, can also be hijacked bya deceptively simple virus and points to a need for a better under-standing of how the system behaves among various hosts (bats, andhumans with diverse HLA types).

§ Signaling Games: Signaling Games are multi-player (usually,two players) games with incomplete information: specifically, one

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player is informed and the other player is not. The informed player’sstrategy set consists of signals contingent on information Uninformedplayer’s strategy set consists of actions contingent on signals.

§ Game: is played as follows1. Player S is assigned a type t ∈ T2. S send to player R a signal s ∈ M.3. R takes an action a ∈ A.

Payoff function: The utility functions for sender and receiver aredependent on the type of the sender, signal sent and action carriedout by the receiver:

ui∈{S,R} : T ×M× A→ R.

Immune System Glossary (Cont.):Antibody An important part of the

Adaptive Immune System. It is aprotein usually in the blood anddestroys or neutralizes bacteria,viruses, or other harmful toxins.Antibody production takes place inresponse to antigen. They are mem-bers of a class of proteins knownas immunoglobulins, produced byB-Cells in response to stimulation byan antigen.

Antigen A substance antagonizingthe immune system to produceantibodies.

Antigen Presenting Cell (APC) A whiteblood cell that engulfs foreign bod-ies, breaks them down, and carriescharacteristic antigen peptides to itssurface. The foreign antigen, com-plexed with MHC I or II (specificto host’s HLA type) is presented toCD4 or CD8 to initiate an immuneresponse specific to that peptide.

B-Lymphocytes (B-Cells) B-lymphocytesare blood cells derived from thebone marrow and spleen involved inthe production of antibodies. B-Cellsproduce antibodies, when primedby T-Cells. B-Cells lymphocytescan later differentiate into plasmaand memory cells. In our signalinggame, they are modeled as recom-menders and accelerate convergenceto a separating NE based on the pastmemory of encounters.

CD-4 Cell “Helper” T-cell, coordinatesmuch of the adaptive immuneresponse.

Cytokine A signaling molecule, actingas a chemical messenger releasedby white blood cells, includingmacrophages, monocytes or lym-phocytes. The cytokines include theinterferons, the interleukins, Tumornecrosis factor, etc.

§ Equilibrium Concept:Behavior Strategies for Senders and Receivers:

1. For S a function µ : T ×M→ [0, 1] such that

∑s∈M

µ(t, s) = 1, for all t.

µ(t, s) = Probability that S with type t sends signal s.2. For R a function α : M× A→ [0, 1] such that

∑a∈A

α(s, a) = 1, for all s.

α(s, a) = Probability that R takes action a following signal s.We may then say that the receiver may acquire a subjective proba-

bility distribution over T.

β(t, s) =µ(t, s)π(t)

∑t′∈T µ(t′, s)π(t′)

Nash Equilibria

Proposition: Behavior strategies (α∗, µ∗) form a Nash equilibrium ifffor all t ∈ T

µ(t, s) > 0 implies

∑a∈A

US(t, s, a)α(s, a)

= maxs′∈S

∑a∈A

US(t, s′, a)α(s′, a);

& for all s ∈ S (s.t. ∑t∈T µ(t, s)π(t) > 0)

α(s, a) > 0 implies

∑t∈T

UR(t, s, a)β(t, a)

= maxa′∈A

∑t∈T

UR(t, s, a′)β(t, a′).

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§ Signaling Games in Nature: In order to assume reasonableutility functions, we use two natural maps that relate the sender’sprivate information to receiver’s action that would be desirable viaRate Distortion functions combining I(·, ·) (mutual information orrate) with a distortion d·(·, ·) combined using suitable Lagrangeparameters λ·:• Mapping Types and Actions into Signals:

f S : T → A; f R : A→ T.

• SenderUS = I(T, M) + λSdS( f S(t), a).

• ReceiverUR = I(A, M) + λRdR(t, f R(a)).

Deception

Immune System Glossary (Cont.):Dendritic Cell An antigen-presenting

immune cell. They have elongated,tentacle like branches to trap foreignobjects.

Immunoglobulin A protein that acts asan antibody to fight off pathogens.There are 5 classes: IgG, IgA, IgD,IgM and IgE. Recombinant andpooled immunoglobulins fromblood donations are being used tofight off SARS-Cov-2 infection.

Interferons A family of proteins (lym-phokines), secreted by infected hostcells to protect uninfected cells fromviral infections.

HLA The human leukocyte antigen(HLA) complex is a group of relatedproteins, encoded by the majorhistocompatibility complex (MHC)in humans. HLA genes are highlypolymorphic with means that theyhave many different alleles, allow-ing them to fine-tune the adaptiveimmune system - differently fordifferent individuals. HLAs corre-sponding to MHC class I (A, B, andC), present peptides from inside thecell. Foreign antigens presented byMHC class I attract T-lymphocytescalled killer T-cells.

Macrophage A large scavenger cellthat ingests degenerated cellsand secretes messenger proteins(monokines) involved in inflamma-tory reactions, lymphocyte activa-tion and acute systemic immuneresponses.

Memory T Cell Persistent T cells thatbear a receptor for a specific antigenthat was previously encountered inthe course of illness or vaccination.It plays a role of a verifier to ensuresafe execution of the signaling game.

Neutralizing Antibody An antibodythat neutralizes (renders harmless)the infectivity of microorganisms,particularly viruses.

Phagocytosis The consumption anddestruction of foreign materials bywhite blood cells like macrophages.

§ The Model of Signaling Games: The game thus involves twoplayers, namely

S − Sender (Informed)

R − Receiver (Uninformed)

• Their roles can be shared; S may only have partial information;and R may be allowed to perform distributed actions.

• A notion of TYPE, T private to S: is captured by a random variablet whose support is given by T (known to Sender S). π(·) = Prob-ability distribution over T is a prior belief of R that the sender’stype is t.

§ Subjective Reality:• Note that the distribution of signals received by R is given by the

probability distribution πM, where

πM(s) = ∑t∈T

πT(t)µ(s|t),

• And the distribution of actions produced by R is given by theprobability distribution πA, where

πA(a) = ∑s∈M

πM(s)α(a|s).

• Clearly πT and πA are probability distributions on T and A re-spectively. If πT is the probability distribution on T induced by πA

under the function fR, then

πT(·) := πA( f−1R (·)). (1)

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A natural choice of measure of deception may be given by therelative entropy between the probability distributions πT and πT :

Deception := Rel. Entropy(πT |πT)

= ∑t∈T

πT(t) log2πT(t)πT(t)

. (2)

This definition describes deception from the point of view of thereceiver. To get the notion of deception from the point of view of thesender, one needs to play the game several rounds.

Thus Signaling Games may reach a Nash equilibrium that is stablebut not deception-free (e.g., immune system may reach a homeostasisthat may not be ideal in separating self from non-self).• If the game reaches a Separating Equilibrium then: Each type t

sends a different signal Mt. f S : t 7→ a[Mt]...• If on the other hand, the game reaches a Pooling Equilibrium: All

types t send a single signal s∗ with probability 1.• Convention & Deception: The divergence between the objective

probabilities and the subjective probabilities induced by conven-tional equilibria.

• Solution: Costly Signaling; Credible and Non-credible threat;Aligned Utilities; Augmenting with additional non-strategic play-ers – denoted as: m Recommenders + n Verifiers

Immune System Glossary (Cont.):T Cells (T Lymphocytes) A thymus

derived white blood cell that pre-cipitates a variety of cell mediatedimmune reactions. Three funda-mentally different types of T cellsare recognized: helper, killer, andsuppresser (each has many subdi-visions). They can be modeled asverifiers in the signaling game.

T Helper Cells Lymphocytes responsi-ble for assisting other white bloodcells in responding to infection,processing antigen, and triggeringantibody production (also known asT4 cells, CD4 cells).

T Killer Cells A major component of cy-totoxic lymphocyte response (CTL),responsible for lysing infected orcancerous cells, T killer cells (not tobe confused with natural killer cells)are a subset of CD8+ lymphocytes.

T Suppressor Cells T lymphocytesresponsible for turning the im-mune response off after infection iscleared, a subset of CD8+ lympho-cytes.

The possibility of deception (e.g., biomimicry by SARS-Cov2) inthe Nash equilibrium (NE) of the signaling game may be the rea-son why the Innate immune system (with PAMP and DAMP) is notthe ultimate solution; the NE must be stable, but also keep up withrapidly evolving pathogens. It leads to a need for an adaptive im-mune system, training of T-cell by DC, chemo-taxis and maturationprocesses that DC must go through, cytokine storms, etc. So “it isvery complicated..” and more so if we need to create a vaccine thatmust deceptively mimic the virus, which may have been alreadydeceptively mimicking the host system, And the vaccine must becarefully analyzed and regulated so as not to catalyze autoimmunedisorders or antigen dependent enhancement ADE.

Quo Vadis: Covid

Covid-19 poses a wicked problem. “The repeated game it plays –covid game – has long and branching chains, intertwined hierarchies,plenty of room for deception and explosive growth rates. Similar fea-tures were needed in the counter measures to tame it5–” A propor- 5 L. Rudolph: personal comm. 2020

tionally rapid and rigorous analysis of the game as well as synthesisof hyper-local policies (e.g., strategies) addressing molecular, indi-vidual and community-wide actions. For argument’s sake, assuming

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that it only manifests as a socio-economic question, it remains un-fathomable what economic utilities might be ethically and equitablytraded off for loss and depreciation of human capital.

Figure 3: Viral Arrival and its Rivalriesin Many Scales: Covid poses a wickedproblem affecting different human or-gan, physical and social systems at dif-ferent spatio-temporal scales. RxCoveaattempts to solve this wicked problemat all scales in an integrative man-ner. Note that Wiki defines “a wickedproblem as a problem that is difficultor impossible to solve because of in-complete, contradictory, and changingrequirements that are often difficultto recognize. ... Another definition is‘a problem whose social complexitymeans that it has no determinablestopping point.’ Moreover, because ofcomplex inter-dependencies, the effortto solve one aspect of a wicked problemmay reveal or create other problems.’Covid problem started as a healthcareproblem, but quickly evolved into aneconomic problem, triggering variousissues related to humans’ fundamentalrights. Courtesy: R.x. Covea et al.

Many of the unknown unknowns are exacerbated by the impactsof unquantified — or unquantifiable — (1) proportion of asymp-tomatic patients, (2) comorbidities and vulnerability of various sub-populations, (3) co-evolution of the disease in the presence of others(flu or multiple strains – with unknown cross immunity) , (4) num-ber and combinatorial structure of the network of super-spreaders,(5) individual boundedly-rational compliance, (6) spatio-temporalreaction-diffusion nature of the disease (e.g., Turing Labyrinth forherd immunity), (7) accuracy, frequency and scaling of biomedi-cal tests (separating asymptomatic from symptomatic, susceptiblefrom infected and infected from immune, etc.), (8) unpredictabil-ity of treatment and preventive measures such as social-distancing,contact-tracing, repeated lock-downs, and quarantines, (9) alloca-tion of resources for patients across vulnerabilities, demographics,genders and races, etc. RxCovea has sought to develop and openlydisseminate mathematical and computational tools and theories toaddress these problems with the help of modelers (SDE’s, graph-based, hybrid, cellular automata), game theorists (signaling games,minority games), logicians (formal methods, model checkers, beliefrevision), algorithmicists (multi-objective decision and optimizationproblems), statisticians (bandit problems, reinforcement learning)and computational systems biologists (in Silico vaccine and drugdiscovery).1) 100 nm Scale: Virology – A task group (“la famiglia”), consisting

of Salvatore Alaimo, Eva Bischof, Jantine Broek, Ashley Duits,Alfredo Ferro, Naomi Maria, Alfredo Pulvienti, Valentina Rapi-cavoli, has been studying the systems biology of the virus andhost-pathogen interactions. The group has been able to replicatein silico – safely, scalably and inexpensively – a large class ofin vivoand in vitro experiments to test a substantial number of hypothesesregarding host-pathogen-drug interactions. Rigorous statisticalanalysis, to correct for multiple hypotheses testing, then points tothe strategies (possibly involving deceptive bio-mimicry) that thevirus may evolve and how drugs may be repurposed to enable thehost organs, systems and pathways to counter safely. The groupalso aims to investigate how SARS-Cov2 virus achieves a symbioticexistence with other reservoir hosts (e.g., bats and pangolines) andhow its genome mutates in order that hosts’ immune system mayaccommodate such a (“pooling”) Nash equilibria (perhaps, withconstrained antigenic drift). Another task group (“the gamers”)consisting of William Casey and Steven Massey has developed

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models of biomimicry (especially the ones achieved by SARS-Cov-2, mimicking Polybasic Cleavage Site, PCS mutations to interactwith host furins) that speaks to intelligent and safe vaccine anddrug design. Marco Antoniotti has been studying the Covid Strainmutations, Tamar Schlick, its genomic chemical structure andCharles Cantor, sophisticated multi-color PCR testing methods,tracking the viral mutations

2) 1 µm Scale: Immunology – Another task group (“the adaptors”) hasbeen studying the host immune system’s response to viral infec-tion: the group consists of James Bannon, Charles Cantor, AshleyDuits, John Conolloy, Kelly Ganjei, Jia Han and Mike Lotze andit analyzes longitudinal adaptomic data from patients, using tem-poral network analysis using advanced combinatorics and formalmethods. It is desired, with the availability of adequate resources,to expand the team to study the genomic markers stratifying theprobands, who exhibit a wide range of symptoms – asymptomaticvs symptomatic or super-spreaders or Kawasaki/MISC diseasephenotypes. It is conjectured that the immunogenic biomark-ers can be characterized by a GWAS (Genome Wide Associa-tion Study), if certain genomic regions (e.g., p-arm of Chr 6) aremapped haplotypically with long range single molecule technol-ogy such as nanomapping. Possible biomarkers clustering aroundHLA, KIR and TLR regions are being studied by a group consist-ing of Marcin Imilienski, Sanjan Kumar, Jason Reed and AmirToor. Vijay Chandru and Ramesh Hariharan are aiming to ini-tiate a similar project in India, which enjoys a more interestingadmixture population, driven by endogamy (“the grandest geneticexperiment ever performed on man,” according to TheodosiusDobzhansky.)

Figure 4: YACHT’s performance on auniversity campus with five dorms. Thestudent population is simplified to beheterogeneous with two assumed im-munogenic biomarkers: e.g., HLA types‘HLA-A’ and ‘HLA-B,’ where agents oftype ‘HLA-A’ are less infectious than’HLA-B’ agents. Simulation assumesthere is only one viral strain. (PanelA) Observe that increasing pool sizesdecreases the total number of infectionswhile increasing quarantining. Aftera delay, the quarantined time also re-duces. (Panel B) Shows the SIR plot ofthe same simulated system with exactly15 pools per dorm. Observe that theprevalence is easily controlled to below5%. Courtesy I. Enaganti et al.

3) 100 m Scale: Epidemiology/Social Immunology – RxCovea’s third taskgroup (“the labyrinthers”) has focused on various epidemiolog-ical models and their parametric control using clever (pool- andindividual-) testing methods with low latency: the group com-prises Ved Basu, Jantine Broek, Shireshendu Chatterjee, InavamsiEnaganti, Hilary Gao, Eva Guo, Mathew Jacobs, Kim Mishra (formodeling) and Charles Cantor, Vijay Chandru, Manoj Gopalakr-ishnan, Inavamsi Enaganti, Satyajit Mahrana, Rohit Nandwani (fortesting); the two subgroups cross-pollinate intimately. The sub-groups started with standard Cellular Automata (CA)agent-basedmodel for incorporating geographical distributions of infectionand easily captures the notion of discrete pairwise interactions,since the new state of a Cellular Automaton (CA) is based on itscurrent state and the states of its surrounding CAs as well as somecommon evolving rules. The infection spreads from an infected

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CA to adjacent neighbouring CAs, while infected patients alsorecover and become immune to the reinfection.

Figure 5: Epidemiological Model – e.g.,compartmental models such as SIRwith compartments: S (susceptible),I (infected) and R(removed). The di-agram shows why the uncertaintiesin parameters may make the modelsunpredictable - especially, when popu-lation is of finite size. Still the modelscan be used fruitfully to stress testvarious plausible policies and affectboundedly rational agent behaviors. –Courtesy: J. Broek et al.

We have assumed the following states for the population Exposed,Symptomatic, Asymptomatic, Susceptible, Recovered/Immune– further augmented with such other states as: unknown, tested,vaccinated, quarantined, retested, recurrent, etc., with respect toother SARS-Covs and flu. RxCovea has also implemented CTMC(continuous time markov chain) and realistic SDE (stochastic dif-ferential equation) models – the later model obtained by usingTuring’s reaction-diffusion equation framework and the analysis ofits solutions - e.g., Turing labyrinths.We conjecture that the formation of Turing Labyrinths (possiblyfurther stratified by HLA’s and Cov2-strains) will play a role inthe formation of herd immunity, vaccination and social distanc-ing policies. These pattern formations can be further moulded byRNA, antigen and immunoglobulin tests (YACHT, Yet AnotherCovid-Health Testing) 6, as well as contact tracing (with 1 or 2 de- 6 In YACHT’s simplest incarnation:

• A user is recommended a pool inwhich their saliva can be testedwithin a time interval:

• If the user selects to be pool-testedand the pool-test result is negative,the user is given a badge (non-counterfeitable plastic wrist- tag,encrypted electronic badge or acrypto-coin tag) that lasts a pre-determined period. During thatperiod with the safe badge, the usermay be allowed to enter (resp. exit)certain safe (resp. unsafe) locations.

• If, on the other hand, the user selectsto be pool-tested and the pool-testresult for the user is positive, thenthe user is given an unsafe badge– and recommended a uniformlyrandomly selected pool (Hot-Potatoprotocol) and/or exponentiallyrandomly selected time interval(Exponential-Back-off protocol) forbeing retested. The user without asafe-badge is virtually quarantinedfrom entering a safe region (orleaving unsafe region - whichmust have sheltering-in-place orhospitals).

• Also since the subsequent choices ofthe pools are (by recommendation)independent, if the user is trulynegative, they will be determinedso (almost surely) no later thana fixed run-length of “(apparent)false-positive” results. If a user failsto be negative after fixed run-lengthof “(apparent)-true-positive” results,the user must be quarantined.

grees of separation) both operated at a large scale with a selectedperiodicity. The original YACHT design motivated by the follow-ing game-theoretic model: (i) Repeated Game: Repeated saliva pooltesting (involving hundreds of individuals in a pool) using rapidand accurate (duplicated) PCR test is feasible with negligible falsenegatives and manageably low false positive. (ii) Private Game/NoIntermediary: Sample collection must remain safe, unsophisticated,ubiquitous and unbiased (from self-selection) and thus may notinvolve robotics and technicians. (iii)Decentrality: Data collectionand storage must be reliable, private and yet not centralized. (iv)Factual and Counter-factual: The analysis is flexible, hypotheses-testable, easy-to-communicate and adaptive in controlling com-pliance, prevalence, immunization and resource usage. YACHT’sresemblance to Ethernet’s Aloha protocol and PageRank’s randomsurfer approach, especially with small/moderate prevalence, addsto our faith in its robustness. We have simulated a model, withpromising results, that partition the population into two regions(“home” encountering both safe and unsafe household membersand “work” encountering safe non-household members) and as-sumes that the household statistics differ from country to country(India, Afghanistan, USA, and Netherlands). In the near future, wewish to resimulate the system with one additional region: “chal-lenge region,” which may be factual or counter factual (e.g., withvirtual viral strains and spreading and testing mechanisms) andallow collection of statistical data for hypotheses testing.

4) 100 km Scale: Logic, Inference and Learning – The fourth task group(“the model checkers”) is a data-science group to delineate the

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causal structures among various pandemic related events; thegroup includes: Marco Antoniotti, Jantine Broek, Daniel Cage,Will Casey, Shirshendu Chatterjee, Vijay Chandru, James Edmond-son, Yaron Gvili, Stella Luna, Ramon Luna and Larry Rudolph.The group is preparing for a near future when massive amountof meta-data, (e.g., involving pools, mobility and geographic oc-cupancy data – from FourSquare) can be combined with MachineLearning tools augmented with Formal Methods to hypothesizeand test causal relationship and intervention strategies. Since ourgames include complex subgames involving credible and non-credible threats, monitoring human behavior – without assumingperfect rationality – is likely to play a critical role. We plan to useProb-prog tools (Julia/Turing7) to understand the disease etiology, 7 A probabilistic programming software

package, named after the computerscientist and logician Alan Turing.

and individuals’ strategic choices tempered by the knowledge ofcausality, time, logic and games, privacy, reputation, trust, decep-tion, and cellularuzation.

5) 1000 km Scale: Economics and Normative Equilibria – The “OpenSim,” group (including Ved Basu, Jantine Broek, Will Casey, Shir-shendu Chatterjee and Yaron Gvili) is studying how to connectcomponents of global data to infer effect of stratification of popu-lations based on demographics, age, gender, genomics (e.g., HLA),(co-)morbidity, etc. to understand genuine causal structures onlyusing natural experimental data and without getting bogged downby the bias due to multiple hypotheses testing and Simpson’seffect. The economic roles played by the disrupted interrelation-ships among different subgroups (and their possible simulationby digital means, when individuals need to be socially distanced)have a strong impact on the V or W shaped economic recovery.The “Burpa group” (comprising Kose John, Samir Saadi, CherylQi) has designed a novel market microstructure to enable healthinsurance for a patient population (social-network) interactingwith scientists and clinicians (expert-network) to create digitalhealthcare markets that tame its risks by combining multiple SPV’s(Special Purpose Vehicles) and securitization

Pavamana (Purification)

Figure 6: pavamana abhyaroha: Pu-rification Prayers; The mantra wasoriginally meant to be recited duringthe introductory praise of the Somasacrifice by the patron.

In a more optimistic future, to which we hope to return soon, Rx-Covea will focus on better algorithms for randomly-surfing explain-able AI’s to create a world-wide adaptive immune system to protecthumans and things physiologically, physically and digitally. Theadaptive learning recommenders and verifiers will be able to an-ticipate and create mitigating plans for future zoonotic events. Fornow, our collective afforts aim to provide computational models of

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host-pathogen interactions that will help define parameters criticalto health-care policies and methods to control the viral spread – “thehammer and the dance.” We hope that optimistic future will alsoinclude a successful completion of Human Hapoltypic HLA Genomeproject, making it unfashionable among immunologists to say, “Thething is, the immune system is very complicated... !”

Acknowledgement

In mid-March of 2020, spurred by a hypothesis centered aroundHLA-heterozygotic advantages of asymptomatic Covid patients, weorganically converged to form the “cure COVid-19 for Ever and ForAll” (RxCovea) Group8, a rigorous community of scientists, clini- 8 The group (RxCovea) benefits from the

experience of Gideon Berger (Sr. MD,Black Stone), Daniel Cage (CEO, Speed-Chain), Charles Cantor (Founder of theHuman Genome Project, ex-CTO Se-quenom), Vijay Chandru (Co-Founder,Strand), Ashley Duits (Red Cross BloodBank Foundation Curaçao, Willemstad,Curaçao and Curaçao Biomedical &Health Research Institute, Willemstad,Curaçao), Inavamsi Enaganti (Depart-ment of Computer Science, Courant In-stitute, NYU), J. Kelly Ganjei (CognateBioServices Inc), Jian Han (FounderiReportoire), Ramesh Hariharan (CEO,Strand Life Sciences), Zurit Levin(CEO, Compugen) Mike Lotze (Asst.Vice Chancellor, Prof. Immunology,UPMC), Sultan Meghji (CEO, Neocova),Thomson Nguyen (Entrepreneur-in-Residence, Kleiner-Perkins), SteliosPapadoupolous (Chairman Biogen),Larry Rudolph (VP, Two Sigma), TariqSamad (Senior Fellow, TechnologyLeader Institute, Ex-Honeywell), TamarSchlick (Prof., NYU), Lex van der Ploeg(CEO, Yao – the Bard, LLC), Chris Wig-gins (Prof, Columbia, CDO, NYT), andAlex Zhavoronkov (Founder/CEO ofInSilico), among 150 others, give or takea few.

cians, AI-specialists, mathematical and computational/data mod-elists, pharmaceutical, public and digital health intelligence represen-tatives from multiple institutions, countries and scientific training.Within the network, self-organized task forces continue to conductcore projects, structured around hypotheses and minimal viableproducts (MVP’s).

Special “thank you”s to Ashley, Charles, Larry, Lex and Vijay –privately “typed” as friends, mentors and mentees – who meticu-lously avoid social-distancing in all the three worlds: The paper hasbenefited a lot from their signals and actions!

The contributions by BM were supported by National ScienceFoundation Grants CCF-0836649 and CCF-0926166, a NationalCancer Institute Physical Sciences-Oncology Center Grant U54

CA193313-01 and a US Army grant W911NF1810427. The contri-butions by RxC have been voluntary and unsupported.

References

[1] Samuel Beckett. Dante ... Bruno, Vico ... Joyce. Our ExagminationRound His Factification for Incamination of Work in Progress, 1929.

[2] Simon M. Huttegger, Brian Skyrms, Rory Smead, and KevinJ. S. Zollman. Evolutionary dynamics of lewis signaling games:signaling systems vs. partial pooling. Synth., 172(1):177–191, 2010.

[3] B. Skyrms. Signals. Oxford University Press, Oxford, 2010.

[4] Ed Yong. Immunology is where intuition goes to die. The Atlantic,2020.

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tamaso mā jyotirgamaya: Seeking the Self Amidst Covids ... · R.x. Covea & B. Mishra tamaso ma jyotirgamaya: Seeking the Self¯ A minuscule subset of the visible physical world is