[PPT] - Membrane Computing: Power, Efficiency, Applications (A Quick PowerPoint Presentation

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Membrane Computing: Power, Efficiency, Applications

(A Quick Introduction)

Gheorghe P˘ aun Romanian Academy, Bucharest, RGNC, Sevilla University, Spain george.paun@imar.ro, gpaun@us.es

Gh. P˘

aun, Membrane Computing. Power, Efficiency, Applications Bertinoro 2008 1

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Summary:

generalities
the basic idea
examples
classes of P systems
types of results
types of applications

– applications in biology – modeling/simulating ecosystems – Nishida’s membrane algorithms – MC and economics; numerical P systems

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Goal: abstracting computing models/ideas from the structure and functioning of living cells (and from their organization in tissues,

rgans, organisms)

hence not producing models for biologists (although, this is now a tendency) result:

distributed, parallel computing model
compartmentalization by means of membranes
basic data structure: multisets (but also strings; recently, numerical variables)
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WHY? – the cell exists! (challenge for mathematics) – biology needs new models (discrete, algorithmic; system biology, the whole cell modelling/simulating) – computer science can learn (e.g., parallelism, coordination, data structure, architecture, operations, strategies) – computing in vitro/in vivo (“the cell is the smallest computer”) – distributed extension of molecular computing – a posteriori: power, efficiency (“solving” NP-complete problems) – a posteriori: applications in biology, computer graphics, linguistics, economics, etc. – nice mathematical/computer science problems

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References:

Gh.

P˘ aun, Computing with Membranes. Journal of Computer and System Sciences, 61, 1 (2000), 108–143, and Turku Center for Computer Science- TUCS Report No 208, 1998 (www.tucs.fi) ISI: “fast breaking paper”, “emerging research front in CS” (2003) http://esi-topics.com

Gh. P˘

aun, Membrane Computing. An Introduction, Springer, 2002

G. Ciobanu, Gh.

P˘ aun, M.J. P´ erez-Jim´ enez, eds., Applications of Membrane Computing, Springer, 2006

forthcoming Handbook of Membrane Computing, OUP
Website: http://ppage.psystems.eu

(Yearly events: BWMC (February), WMC (summer), TAPS/WAPS (fall))

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SOFTWARE AND APPLICATIONS: http://www.dcs.shef.ac.uk/∼marian/PSimulatorWeb/P Systems applications.htm www.cbmc.it – PSim2.X simulator Verona (Vincenzo Manca: vincenzo.manca@univr.it) Sheffield (Marian Gheorghe: M.Gheorghe@dcs.shef.ac.uk) Sevilla (Mario P´ erez-Jim´ enez: marper@us.es) Milano (Giancarlo Mauri: mauri@disco.unimib.it) Nottingham, Trento, Nagoya, Leiden, Vienna, Evry, Ia¸ si

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FRAMEWORK: Natural computing

Cell DNA (molecules) Evolution Brain Neural computing Evolutionary computing DNA(molecular) computing Membrane computing Electronic media (in silico) Bio-media (in vitro, in vivo?)

✲ ✲ ✲ ✲ ❍❍❍❍❍❍❍ ❍ ❥ ✲ ❳❳❳❳❳❳❳❳❳❳❳❳ ③ ✏✏✏✏✏✏✏✏✏✏✏ ✏ ✶ ✡ ✡ ✡ ✡ ✡ ✡ ✣ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄✄ ✗

? ? Biology (in vivo/vitro) Models (in info) Implementation

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FRAMEWORK: Natural computing

Cell DNA (molecules) Evolution Brain Neural computing Evolutionary computing DNA(molecular) computing Membrane computing Electronic media (in silico) Bio-media (in vitro, in vivo?)

✲ ✲ ✲ ✲ ✲ ❍❍❍❍❍❍❍ ❍ ❥ ✲ ❳❳❳❳❳❳❳❳❳❳❳❳ ③ ✏✏✏✏✏✏✏✏✏✏✏ ✏ ✶ ✡ ✡ ✡ ✡ ✡ ✡ ✣ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄✄ ✗

? ? Biology (in vivo/vitro) Models (in info) Implementation

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Gh. P˘

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WHAT IS A CELL? (for a mathematician)

membranes, separating “inside” from “outside” (hence protected compartments,

“reactors”)

chemicals in solution (hence multisets)
biochemistry (hence parallelism, nondeterminism, decentralization)
enzymatic activity/control
selective passage of chemicals across membranes
etc.
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Importance of membranes for biology:. . . MARCUS: Life = DNA software + membrane hardware

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THE BASIC IDEA

✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ★ ✧ ✥ ✦ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪

1 2 3 4 5 6

✚ ✚ ✚ ❂

skin membrane

✟ ✟ ✟ ✟ ✟ ✟ ✟ ✟ ✙

elementary membrane environment

✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✘ ✾

region

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✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪

1 2 3 4 5 6 a b b b c c b b b b a a t t

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✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪

1 2 3 4 5 6 a b b b c c b b b b a a t t ab → ddoutein5 ca → cb d → ain4bout t → t t → t′δ

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Functioning (basic ingredients):

nondeterministic choice of rules and objects
maximal parallelism
transition, computation, halting
internal output, external output, traces
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EXAMPLES

✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪

1 2 c a → b1b2 cb1 → cb′

1

b2 → b2ein|b1 Computing system: n − → n2 (catalyst, promoter, determinism, internal output) Input (in membrane 1): an Output (in membrane 2): en2

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✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪

1 2 c a → b1b2 cb1 → cb′

1

b2 → b2e cb1 → cb′

1δ

b1 → b1 e → eout The same function (n − → n2), with catalyst, dissolution, nondeterminism, external

utput
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✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪ ✬ ✫ ✩ ✪

1 2 3 4

a f a → ab′ a → b′δ f → ff b′ → b b → bein4 ff → f > f → aδ

af 1 ab′ff . . . . . . m ≥ 0 ab′mf 2m m + 1 b′m+1f 2m+1 δ m + 2 bm+1f 2m m + 3 bm+1f 2m−1 em+1

in4

. . . . . . . . . 2m + 1 bm+1f 2 em+1

in4

2m + 2 bm+1f em+1

in4

2m + 3 bm+1aδ em+1

in4

m + 1 times HALT! Generative mode : {n2 | n ≥ 1}

❩❩❩❩❩ ❩ ⑦ ✑ ✑ ✑ ✑ ✑ ✑ ✰

(m + 1) × (m + 1) N(Π) = {n2 | n ≥ 1}

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SIMULATING A REGISTER MACHINE M = (m, B, l0, lh, R)

✬ ✫ ✩ ✪

1 l0 E = {ar | 1 ≤ r ≤ m} ∪ {l, l′, l′′, l′′′, liv | l ∈ B} (l1, out; arl2, in) (l1, out; arl3, in)

for l1 : (add(r), l2, l3)

(l1, out; l′

1l′′ 1, in)

(l′

1ar, out; l′′′ 1 , in)

(l′′

1, out; liv 1 , in)

(livl′′′

1 , out; l2, in)

(livl′

1, out; l3, in)

           for l1 : (sub(r), l2, l3) (lh, out) Symport/antiport rules (of weight 2)

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Types of rules: u → v with targets in v (possibly conditional: promoters or inhibitors) particular cases: ca → cu (catalytic) a → u (non-cooperative) (ab, in), (ab, out) – symport (in general, (x, in), (x, out)) (a, in; b, out) – antiport (in general, (u, in; v, out)) u]iv → u′]iv′ – boundary (Manca, Bernardini) ab → atar1btar2 – communication (Sosik) ab → atar1btar2ccome a → atar

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a[ ]i → [b]i go in [a]i → b[ ]i go out [a]i → b membrane dissolution a → [b]i membrane creation [a]i → [b]j[c]k membrane division [a]i[b]j → [c]k membrane merging [a]i[ ]j → [[b]i]j endocytosis [[a]i]j → [b]i[ ]j exocytosis [u]i → [ ]i[u]@j gemmation [Q]i → [O − Q]j[Q]k separation and others

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Basic classes of cell-like P systems: multiset rewriting P systems: Π = (O, µ, w1, . . . , wm, R1, . . . , Rm, io),

O = alphabet of objects
µ = (labeled) membrane structure of degree m (represented by a string of

matching parentheses)

wi = strings/multisets over O
Ri = sets of evolution rules

typical form ab → (a, here)(c, in2)(c, out)

io = the output membrane

Symport/antiport P systems: Π = (O, µ, w1, . . . , wm, E, R1, . . . , Rm, io), as above, with E ⊆ O the set of objects which appear in the environment in arbitrarily many copies

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A bird eye view to the MC jungle:

cell-like, tissue-like, neural-like (spiking neural) systems
symbols, strings, arrays, numerical variables, etc.
multisets, sets, fuzzy
multiset rewriting, symport/antiport, membrane evolving, combinations
controls: priority, promoters, inhibitors, δ, τ, activators, etc.
maximal, bounded, minimal parallelism, sequential/asynchronous, time-, clock-

free

generating, accepting, computing/translating, dynamical system
computing power, computing efficiency, others
implementations/simulations
applications:

biology/medicine, economics, optimization, computer graphics, linguistics, computer science, cryptography, etc.

etc. (e.g., brane-membrane bridge, quantum-like)
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Results:

characterization of Turing computability (RE, NRE, PsRE)

Examples: by catalytic P systems (2 catalysts) [Sosik, Freund, Kari, Oswald] by (small) symport/antiport P systems [many] by spiking neural P systems [many]

polynomial solutions to NP-complete problems (by using an exponential workspace

created in a “biological way”: membrane division, membrane creation, string replication, etc) [Sevilla team], [Madras team], [Obtulowicz], [Alhazov, Pan] etc even characterizations of PSPACE

other types of mathematical results (normal forms, hierarchies, determinism versus

nondeterminism, complexity) [Ibarra group]

connections with ambient calculus, Petri nets, X-machines, quantum computing,

lambda calculus, brane calculus, etc [many]

simulations and implementations
applications
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Open problems, research topics: Many: see the P page

borderlines: universality/non-universality, efficiency/non-efficiency

(local problems: the power of 1 catalyst, the role of polarizations, dissolution, etc. general problems: uniform versus semi-uniform, deterministic-confluent, pre- computed resources)

semantics (events, causality, etc.)
neural-like systems (more biology, complexity, applications, etc.)
user friendly, flexible, and efficient (!) software for bio-applications
MC and economics
implementations (electronics, bio-lab)
finding a killer-app
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SAQ:

computing beyond Turing? (no, but ...acceleration)
what kind of implementation? (none, but ...Adelaide, Madrid, Technion-Haifa)
why so many variants?
why so powerful? (RE = CS + erasing)
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Applications:

biology, medicine, ecosystems (continuous versus discrete mathematics) [Sevilla,

Verona, Milano, Sheffield, etc.]

computer

science (computer graphics, sorting/ranking, 2D languages, cryptography, general model of distributed-parallel computing) [many]

linguistics (modeling framework, parsing) [Tarragona]
optimization (membrane algorithms [Nishida, 2004], [many])
economics ([Warsaw group], [R. P˘

aun], [Vienna group])

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A typical application in biology/medicine: M.J. P´ erez–Jim´ enez, F.J. Romero–Campero: A Study of the Robustness of the EGFR Signalling Cascade Using Continuous Membrane Systems. In Mechanisms, Symbols, and Models Underlying Cognition. First International Work-Conference on the Interplay between Natural and Artificial Computation, IWINAC 2005 (J. Mira, J.R. Alvarez, eds.), LNCS 3561, Springer, Berlin, 2005, 268–278.

60 proteins, 160 reactions/rules
reaction rates from literature
results as in experiments
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Typical outputs:

10 20 30 40 50 60 0.00 0.04 0.08 0.12 0.16 0.20 0.24 0.28 0.32 time (s) Concentration (nM) 100nM 200nM 300nM

The EGF receptor activation by auto-phosphorylation (with a rapid decay after a high peak in the first 5 seconds)

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20 40 60 80 100 120 140 160 180 1 2 3 4 5 time (s) Concentration (nM) 100nM 200nM 300nM

The evolution of the kinase MEK (proving a surprising robustness of the signalling cascade)

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Other bio-applications:

photosynthesis [Nishida, 2002]
Brusselator [Suzuki, Verona, Milano]
quorum sensing in bacteria [Nottingham, Sheffield, Sevilla]
circadian cycles [Verona]
apoptosis [Ruston-Louisiana]
signaling pathways in yeast [Milano]
HIV infection [Edinburgh]
peripheral proteins [Trento]
others [Milano, Ia¸

si, Bucharest, Sevilla, Verona, etc.]

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Modeling ecosystems

Y. Suzuki, H. Tanaka, Artificial life and P systems, WMC1, Curtea de Arge¸

s, 2000 (herbivorous, carnivorous, volatiles) Lotka-Voltera model (predator-prey) [Verona, Milano]

M. Cardona, M.A. Colomer, M.J. Perez-Jimenez, S. Danuy, A. Margalida,

A P system modeling an ecosystem related to the bearded vulture, 6BWMC

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”Our model consists in the following probabilistic P system of degree 2 with two electrical charges: Π = (Γ, µ, M0, M1, R) where:

In the alphabet Γ we represent the six species of the ecosystem (index i is

associated with the species and index j is associated with their age, and the symbols X, Y and Z represent the same animal but in different state); it also contains the auxiliary symbols B and C. Γ = {Xij, Yij, Zij : 1 ≤ i ≤ 7, 0 ≤ j ≤ ki,5} ∪ { B, C}

In the membrane structure we represent two regions, the skin (where animals

reproduce) and an inner membrane (where animals feed and die): µ = [ [ ]1 ]0 (neutral polarization will be omitted)

In M0 and M1 we specify the initial number of objects present in each regions

(encoding the initial population and the initial food).

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– M0 = {X

qij ij : 1 ≤ i ≤ 7, 0 ≤ j ≤ ki,}, where the multiplicity qij indicates the

number of animals, of species i whose age is j that are initially present in the ecosystem. – M1 = {C B18000}, where the object B represent 0.5 kg of bones, and 9000 kg is the external contribution of bones to the P system corresponding to the 33% of feeding that come from animals do not modeled in the P system.

The set R of evolution rules consists of:

– Reproduction-rules Adult males: r0 ≡ [Xij

1−ki,14

− − − → Yij]0, 1 ≤ i ≤ 7, 0 ≤ j ≤ ki,4 Adult females that reproduce: r1 ≡ [Xij

ki,5ki,14

− − − → YijYi0]0, 1 ≤ i ≤ 7, ki,2 ≤ j < ki,3 Adult females that do not reproduce: r2 ≡ [Xij

(1−ki,5)ki,14

− − − → Yij]0, 1 ≤ i ≤ 7, ki,2 ≤ j < ki,3

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Young animals that do not reproduce: r3 ≡ [Xij → Yij]0, 1 ≤ i ≤ 7, ki,3 ≤ j < ki,2 – Young animals mortality rules: Those which survive: r4 ≡ Yij[ ]1

1−ki,7−ki,8

− − − → [Zij]1 : 1 ≤ i ≤ 7, 0 ≤ j < ki,1 Those which die and leaving bones: r5 ≡ Yij[ ]1

ki,8

− − − →[Bki,12]1 : 1 ≤ i ≤ 7, 0 ≤ j < ki,1

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Those which die and do not leave bones: r6 ≡ Yij[ ]1

ki,7

− − − →[ ]1 : 1 ≤ i ≤ 7, 0 ≤ j < ki,1 – Adult animals mortality rules: Those which survive: r7 ≡ Yij[ ]1

1−ki,9−ki,10

− − − → [Zij]1 : 1 ≤ i ≤ 7, ki,1 ≤ j < ki,4 Those which die leaving bones: r8 ≡ Yij[ ]1

ki,10

− − − →[Bki,13]1 : 1 ≤ i ≤ 7, ki,1 ≤ j < ki,4 Those which die and do not leave bones: r9 ≡ Yij[ ]1

ki,9

− − − →[ ]1 : 1 ≤ i ≤ 7, ki,1 ≤ j < k1,4 Animals that die at an average life expectancy: r10 ≡ Yij[ ]1 → [Bki,13·ki,11]1 : 1 ≤ i ≤ 7, j = ki,4 – Feeding rules: r11 ≡ [ZijBki,16]1 → Xij+1[ ]+

1 : 1 ≤ i ≤ 7, 0 ≤ j ≤ ki,4

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– Rules of mortality due to lack of food, and the elimination from the system of bones that are not eaten by the Bearded Vulture: Elimination of remaining bones: r12 ≡ [B]+

1 → [ ]1

External contribution that represent the bones: r13 ≡ [C]+

1 → [CB18000]1

Adult animals that die because they have not enough food: r14 ≡ [Zij]+

1 → [Bki,13·ki,11]1 : 1 ≤ i ≤ 7, ki,1 ≤ j ≤ ki,4

Young animals that die because they have not enough food: r15 ≡ [Zij]+

1 → [Bki,12·ki,11]1 : 1 ≤ i ≤ 7, j < ki,1

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Figure 1 gives a schematic view of how the P system works. Figure 1: Schema

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Table 1: Number of animals, at the moment, in the Pyrenean Catalan Species Number Bearded Vulture 74 Chamois 12000 Red deer female 4400 Red deer male 1100 Fallow deer 900 Roe deer 10000 Sheep 200000

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(Some) Results:

Bearded Vulture

20 40 60 80 100 120 140 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year Number animals Mortaliy- Feeding- Reproductivity Reproductivity- Mortality- Feeding

Chamois

10000 20000 30000 40000 50000 60000 70000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Year Number animals Mortaliy- Feeding- Reproductivity Reproductivity- Mortality- Feeding

Fallow Deer

500 1000 1500 2000 2500 3000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years Number animals Mortaliy- Feeding- Reproductivity Reproductivity- Mortality- Feeding

Roe Deer

20000 40000 60000 80000 100000 120000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years Number animals Mortaliy- Feeding- Reproductivity Reproductivity- Mortality- Feeding

Sheep

180000 185000 190000 195000 200000 205000 1 2 3 4 5 6 7 8 9 10 1112 13 1415 16 1718 19 20

Years Number animals

Mortaliy- Feeding- Reproductivity Reproductivity- Mortality- Feeding

Red Deer

1000 2000 3000 4000 5000 6000 7000 8000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Years Number animals Mortaliy- Feeding- Reproductivity (Female) Reproductivity- Mortality- Feeding (Male) Mortaliy- Feeding- Reproductivity (Female) Reproductivity- Mortality- Feeding (Male)

Figure 2: Robustness of the ecosystem

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Nishida’s membrane algorithms:

candidate solutions in regions, processed locally (local sub-algorithms)
better solutions go down
static membrane structure – dynamical membrane structure
two-phases algorithms

Excellent solutions for Travelling Salesman Problem (benchmark instances)

rapid convergence
good average and worst solutions (hence reliable method)
in most cases, better solutions than simulated annealing

Still, many problems remains: check for other problems, compare with sub- algorithms, more membrane computing features, parallel implementations (no free lunch theorem) Recent: L. Huang, N. Wang, J. Tao; G. Ciobanu, D. Zaharie; A. Leporati, D. Pagani;

M. Gheorghe et al. (quantum-membrane-algorithms)
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Applications in economics:

J. Bartosik, W. Korczynski, etc (accounting, human resource management, etc)
Gh. P˘

aun, R. P˘ aun (general interpretation, paired rules: ([u → v]i; [u′ → v′]j)

Gh. P˘

aun, R. P˘ aun: Numerical P systems

R. P˘

aun: Modelling producer-retailer transactions

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✬ ✫ ✩ ✪

S bn1

1 , bn2 2 , . . . , bnk k

cm1

1 , cm2 2 , . . . , cml l

C Source of raw materials (a) Producers (d) Retailers (match d with ¯ d) Consumption ( ¯ d)

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Examples of rules:

1. S → SaN±rg[prob(rg)] (no money)
2. biupS(t)

i

a → diupS(t)

S

(producers pay for a)

3. C → C ¯

dM±rg′upC(t)(M±rg′)

C

[prob(rg′)] (the general consumer introduces both needs and money)

4. cj ¯

du

psj(t) C

→ ¯ djv

psj(t) j

(orders and money pass to retailers)

5. di ¯

djvppi(t)

j

→ bicjuppi(t)

i

[Rscorei,j(t)] (one copy of d is purchased by Rj from Pi, paying for it the price pi(t) set by Pi)

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Still more interesting: investments ux

i → bi – by producer i

vy

j → cj – by retailer j

maybe in a bounded amount fiux

i → bi

gjvy

j → cj

with z copies of each fi and gj introduced in the initial configuration

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What about future? (at the edge of science-fiction)

hard to predict the future...
...but the progresses should not be underestimated
natural computing will pay-off (directly, or through by-products)
e.g., through nano-technology
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SLIDE 49

Every attempt to employ mathematical methods in the study of biological questions must be considered profoundly irrational and contrary to the spirit of biology. If mathematical analysis should ever hold a prominent place in biology - an aberration which is happily almost impossible - it would

ccasion a rapid and widespread degeneration of that science.

Auguste Comte (full name: Isidore Marie Auguste Franois Xavier Comte; January 17, 1798 - September 5, 1857): Pilosophie Positive, 1830

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SLIDE 50

Dreams:

efficiency (through massive parallelism, nondeterminism)
robust computers/algorithms
adaptable, evolvable, learning, self-healing hardware/software
nano-robots (for medicine)
computing beyond Turing (stronger consequences than P = NP)
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SLIDE 51

Do we dream too much?

nature has different goals (and resources: time, materials, energy), is redundant,

cruel

theoretical limits:

– Conrad theorems (programmability/universality, efficiency, learnability are contradictory) – Gandy principles for computing mechanisms (preventing the possibility to go beyond Turing)

for modeling/simulating intelligence and life, maybe something essentially new is

necessary (Mc Carthy, Brooks, etc.)

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SLIDE 52

Thank you!

...and please do not forget: http://ppage.psystems.eu (with mirrors in China: http://bmc.hust.edu.cn/psystems, http://bmchust.3322.org/psystems)

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