User contributions

Gianfranco

27 September 2022

24 September 2022

Store:Khrennikov04
2. Classical versus quantum probability
17:21
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Formula:Khrennikov006
Created page with "<math>O_1, O_2</math>"
17:20
Talk:Copia di Quantum-like modeling in biology with open quantum systems and instruments
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16:43
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Store:Khrennikov04
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16:41
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Talk:Copia di Quantum-like modeling in biology with open quantum systems and instruments
Created page with " ;Formule {| border="1" cellpadding="8" | |- | F:Khrennikov001 | {{:F:Khrennikov001}} |- | F:Khrennikov002 | {{:F:Khrennikov002}} |- | F:Khrennikov | {{:F:Khrennikov003}} |- | F:Khrennikov | {{:F:Khrennikov004}} |- | F:Khrennikov | {{:F:Khrennikov005}} |- | F:Khrennikov | {{:F:Khrennikov006}} |- | F:Khrennikov | {{:F:Khrennikov007}} |- | F:Khrennikov | {{:F:Khrennikov008}} |- | F:Khrennikov | {{:F:Khrennikov009}} |- | F:Khrennikov..."
16:40
Store:Khrennikov03
Introduction
16:29
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Formula:Khrennikov005
Created page with "<math>[\hat{A},\hat{B}]\neq0</math>"
16:29
Formula:Khrennikov004
Created page with "<math>\hat{B}</math>"
16:28
Formula:Khrennikov003
Created page with "<math>\hat{A}</math>"
16:27
Formula:Khrennikov002
Created page with "<math>B</math>"
16:27
Formula:Khrennikov001
Created page with "<math>A</math>"
16:26
Copia di Quantum-like modeling in biology with open quantum systems and instruments
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16:20
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Store:Khrennikov05
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16:20
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Store:Khrennikov04
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16:19
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Store:Khrennikov03
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16:18
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Store:Khrennikov02
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16:18
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Store:Khrennikov01
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16:18
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Copia di Quantum-like modeling in biology with open quantum systems and instruments
Replaced content with "{{FR | Title = Quantum-like modeling in biology with open quantum systems and instruments | author1 = Irina Basieva | author2 = Andrei Khrennikov | author3 = Masanao Ozawa | Source = https://pubmed.ncbi.nlm.nih.gov/33347968/ | Original =  | Date = 2021<!-- date of the original work, when the author/s published it (dd/m..."
16:17
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Store:Khrennikov16
Created page with "==11. Compound biosystems== ===11.1. Entanglement of information states of biosystems=== The state space <math>{\mathcal{H}}</math> of the biosystem <math>S</math> consisting of the subsystems <math>S_j,j=1,2,....n</math>, is the tensor product of subsystems’ state spaces<math>{\mathcal{H}}_j</math> , so {| width="80%" | |- | width="33%" |'''<big>*</big>''' | width="33%" |<math>\Im=\Im_1\otimes....\otimes\Im_n</math> | width="33%" align="right" |<math>(31)</math>..."
16:16
Store:Khrennikov15
Created page with "==10. Connecting electrochemical processes in neural networks with quantum informational processing== As was emphasized in introduction, quantum-like models are formal operational models describing information processing in biosystems. (in contrast to studies in quantum biology — the science about the genuine quantum physical processes in biosystems). Nevertheless, it is interesting to connect the structure quantum information processing in a biosystem with physical an..."
16:16
Copia di Quantum-like modeling in biology with open quantum systems and instruments
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16:15
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Store:Khrennikov14
Created page with "==9. Epigenetic evolution within theory of open quantum systems== In paper (Asano et al., 2012b), a general model of the epigenetic evolution unifying neo-Darwinian with neo-Lamarckian approaches was created in the framework of theory of open quantum systems. The process of evolution is represented in the form of ''adaptive dynamics'' given by the quantum(-like) master equation describing the dynamics of the information state of epigenome in the process of interaction wi..."
16:14
Store:Khrennikov13
Created page with " ==8. Open quantum systems: interaction of a biosystem with its environment== As was already emphasized, any biosystem <math>S</math> is fundamentally open. Hence, dynamics of its state has to be modeled via an interaction with surrounding environment <math> \varepsilon</math>. The states of <math>S</math> and <math> \varepsilon</math> are represented in the Hilbert spaces <math>\mathcal{H}</math> and <math>\mathcal{H}</math>. The compound system <math>S+\varepsilon<..."
16:14
Store:Khrennikov12
Created page with "==7. Genetics: interference in glucose/lactose metabolism== In paper (Asano et al., 2012a), there was developed a quantum-like model describing the gene regulation of glucose/lactose metabolism in Escherichia coli bacterium.11 There are several types of E. coli characterized by the metabolic system. It was demonstrated that the concrete type of E. coli can be described by the well determined linear operators; we find the invariant operator quantities characterizing each..."
16:13
Store:Khrennikov11
Created page with "==6. Modeling of cognitive effects== In cognitive and social science, the following opinion pool is known as the basic example of the order effect. This is the Clinton–Gore opinion pool (Moore, 2002). In this experiment, American citizens were asked one question at a time, e.g., :<math>A=</math> “Is Bill Clinton honest and trustworthy?” :<math>B=</math> “Is Al Gore honest and trustworthy?” Two sequential probability distributions were calculated on the basis o..."
16:12
Store:Khrennikov10
Created page with "==5. Modeling of the process of sensation–perception within indirect measurement scheme== Foundations of theory of ''unconscious inference'' for the formation of visual impressions were set in 19th century by H. von Helmholtz. Although von Helmholtz studied mainly visual sensation–perception, he also applied his theory for other senses up to culmination in theory of social unconscious inference. By von Helmholtz here are two stages of the cognitive process, and they..."
16:11
Store:Khrennikov09
Created page with "==4. Quantum instruments from the scheme of indirect measurements== The basic model for construction of quantum instruments is based on the scheme of indirect measurements. This scheme formalizes the following situation: measurement’s outputs are generated via interaction of a system <math>S</math> with a measurement apparatus <math>M</math> . This apparatus consists of a complex physical device interacting with <math>S</math> and a pointer that shows the result of me..."
16:11
Store:Khrennikov08
Created page with "===3.4. General theory (Davies–Lewis–Ozawa)=== Finally, we formulate the general notion of quantum instrument. A superoperator acting in <math display="inline">\mathcal{L}(\mathcal{H})</math> is called positive if it maps the set of positive semi-definite operators into itself. We remark that, for each '''<u><math>x,\Im_A(x)</math></u>''' given by (13) can be considered as linear positive map. Generally any map<math>x\rightarrow\Im_A(x)</math> , where for each <m..."
16:10
Store:Khrennikov07
Created page with "===3.3. Non-projective state update: atomic instruments=== In general, the statistical properties of any measurement are characterized by # the output probability distribution <math display="inline">Pr\{\text{x}=x\parallel\rho\}</math>, the probability distribution of the output <math display="inline">x</math> of the measurement in the input state <math display="inline">\rho </math>; # the quantum state reduction <math display="inline">\rho\rightarrow\rho_{(X=x)} </ma..."
15:15
Copia di Quantum-like modeling in biology with open quantum systems and instruments
3.3. Non-projective state update: atomic instruments
15:15
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Copia di Quantum-like modeling in biology with open quantum systems and instruments
3.2. Von Neumann formalism for quantum observables
15:13
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Store:Khrennikov06
Created page with "===3.2. Von Neumann formalism for quantum observables=== In the original quantum formalism (Von Neumann, 1955), physical observable <math>A</math> is represented by a Hermitian operator <math>\hat{A}</math> . We consider only operators with discrete spectra:<math>\hat{A}=\sum_x x\hat{E}^A(x)</math> where <math>\hat{E}^A(x)</math> is the projector onto the subspace of <math display="inline">\mathcal{H}</math> corresponding to the eigenvalue <math display="inline">x</..."
15:12
Copia di Quantum-like modeling in biology with open quantum systems and instruments
3.1. A few words about the quantum formalism
15:11
−2,472
Store:Khrennikov05
Created page with "===3.1. A few words about the quantum formalism=== Denote by <math display="inline">\mathcal{H}</math> a complex Hilbert space. For simplicity, we assume that it is finite dimensional. Pure states of a system <math>S</math> are given by normalized vectors of <math display="inline">\mathcal{H}</math> and mixed states by density operators (positive semi-definite operators with unit trace). The space of density operators is denoted by <math>S</math> (<math display="inli..."
15:10
Copia di Quantum-like modeling in biology with open quantum systems and instruments
2. Classical versus quantum probability
15:06
−3,399
Store:Khrennikov04
Created page with " CP was mathematically formalized by Kolmogorov (1933)<ref name=":2" /> This is the calculus of probability measures, where a non-negative weight <math>p(A)</math> is assigned to any event <math>A</math>. The main property of CP is its additivity: if two events <math>O_1, O_2</math> are disjoint, then the probability of disjunction of these events equals to the sum of probabilities: {| width="80%" | |- | width="33%" |&n..."
15:06
Copia di Quantum-like modeling in biology with open quantum systems and instruments
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14:49
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Store:Khrennikov03
Created page with " The standard mathematical methods were originally developed to serve classical physics. The real analysis served as the mathematical basis of Newtonian mechanics (Newton, 1687)<ref>{{cita libro | autore = Newton Isaac | titolo = Philosophiae naturalis principia mathematica | url = https://archive.org/details/bub_gb_6EqxPav3vIsC | volume = | opera = | anno = 1687 | editore = Benjamin Motte | città = London UK | ISBN = | DOI = | PMID..."
14:48
Copia di Quantum-like modeling in biology with open quantum systems and instruments
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14:46
−184
Store:Khrennikov02
Created page with " Mathematical formalism of quantum mechanics, Open quantum systems, Quantum instruments, Quantum Markov dynamics, Gene regulation, Psychological effects,Cognition, Epigenetic mutation, Biological functions"
14:45
Copia di Quantum-like modeling in biology with open quantum systems and instruments
Abstract
14:45
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Store:Khrennikov01
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14:44

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