Incompatible Events Research Articles

Modeling mental peculiarities of a decision maker by a Fourier-holography technique

A task of modeling individual mental features of a decision-maker using a Fourier holography setup is considered. The problem is considered for a situation when current conditions of decision-making contradict to the previously learned rule of decision-making logic modeled by the non-cooperative game "Prisoner's Dilemma". The approach to the problem is based on a hypothesis of the correlation between mental features and the properties of the neural network as a material carrier of intelligence. The 6f Fourier holography scheme of the resonant architecture is considered as a three-layer neural network implementing a neuro-physiologically motivated concept of the "excitation ring" proposed by A.M. Ivanitsky. We analytically assess the dependence of the validity limits of the classical total probability formula for a disjunction of incompatible events on the characteristics of low-frequency filters in holograms and the correlation radii of the training image of the basic decision rule. Analytical results are confirmed by results of the numerical simulation.

Stochastic processes in the space of random joint events and equations for transition probabilities of quantum systems

A model of the space of random joint events is constructed. In the space, along with the existence of a symmetric difference of joint events, a new postulate about the existence of a symmetric sum of random joint events is introduced. In the generated space, a stochastic equation of the system motion and an equation for the probabilities of the system transition between two events are constructed. The probability of transition depends on the probabilities of compatibility of two, three, etc. events. The equation is equivalent to the equation of quantum theory if the events are compatible only in pairs. The proposed equation for incompatible events passes into the equation of the Markov chain.

Analysis of the probability of connectivity of a telecommunications network based on the reduction of several non-connectivity events to a union of independent events

Introduction: For large and structurally complex telecommunication networks, calculating the connectivity probability turns out to be a very cumbersome and time-consuming process due to the huge number of elements in the resulting expression. The most expedient way out of this situation is a method based on the representation of a network connectivity event in the form of sums of products of incompatible events. However, this method also requires performing additional operations on sets in some cases. Purpose: To eliminate the main disadvantages of the method using multi-variable inversion. Results: It is shown that the connectivity event of a graph should be interpreted as a union of connectivity events of all its subgraphs, which leads to the validity of the expression for the connectivity event of the network in the form of a union of connectivity events of typical subgraphs (path, backbone, and in general, a multi-pole tree) of the original random graph. An iterative procedure is proposed for bringing a given number of connectivity events to the union of independent events by sequentially adding subgraph disjoint events. The possibility of eliminating repetitive routine procedures inherent in methods using multi-variable inversion is proved by considering not the union of connectivity events (incoherence) degenerating into the sum of incompatible products, but the intersection of opposite events, which also leads to a similar sum. However, to obtain this sum, there is no need to perform a multi-variable inversion for each of the terms over all those previously analyzed. Practical relevance: The obtained analytical relations can be applied in the analysis of reliability, survivability or stability of complex telecommunications networks.

Modeling of quantum-like cognitive phenomena by the Fourier-holography technique under the choice of alternatives

The article is dedicated to the search for a biologically motivated mechanism of the cognitive phenomenon of violation of the classical formula of total probability for the disjunction of incompatible events, which is considered by a number of researchers as a quantum-like phenomenon. A classical mechanism implemented by the 6f Fourier holography scheme of the resonant architecture that does not require reference to quantum mechanics either in its physical nature or at the level of formalism is demonstrated. In the analysis, the decision-making is interpreted as a choice of alternatives by using the non-cooperative game "Prisoner's Dilemma". The approach to the task is based on the search for a mechanism for forming a conditional estimate under a condition that contradicts the rule of monotonous decision logic. It is demonstrated that this estimate, in contrast to the unconditional and conditional one with a non-contradictory condition, is formed by logic with exception. The ring architecture of the holographic setup corresponds to the biologically inspired neural network concept of the excitation ring and implements cognitive dissonance on logic with exception. Conditions and ranges of violation of the classical formula of total probability in relation to the correlation radius of the reference image recorded in a hologram storing the monotone logic inference rule are analytically determined. The analytical model is confirmed by a quantitative coincidence of the results of numerical modeling with the published results of natural experiments.

Paired discrete competition with a free route choice

The paper considers the problem of optimizing the operation schedule for multiprocessor systems. The solution to this problem involves the formation of a rigid work schedule, which determines the rhythm of the processes, but in practice the functioning of systems is influenced by many side factors that make the intervals of work execution random. In the work, a semi-Markov model of the formation of a stochastic schedule in conditions of pair competition is constructed. It is shown that if during the functioning of the system it is possible to execute the items of the schedule in an arbitrary order, then the evolution of the semi-Markov process follows the Hamiltonian path. It is proved that all possible realizations of Hamiltonian paths form a complete group of incompatible events. It is noted that, due to the imposition of restrictions on the nature of evolution, the evolution process is not strictly semi-Markov, and therefore a method of forming a strictly semi-Markov process with a tree structure from the primary model is proposed. Dependences are obtained for calculating the distribution densities and the probabilities of switching from states of a semi-Markov process to conjugate states, as well as the time of walking from the starting to absorbing states. Using the concept of paired discrete competition and a distributed penalty, the effectiveness of the choice of a Hamiltonian path by one of the subjects is estimated, taking into account the fact that the algorithm of his opponent’s behavior is known up to the construction of a semi-Markov model.

Recurring urothelial carcinomas are clonal but incompatible with a direct relationship

To describe the genetic relationship between the primary and recurrent bladder tumors and to identify their origins, different models such as the field cancerization, seeding, and intraepithelial migration have been proposed. The aim of this study was to investigate the genetic relationship in syn- and metachronous bladder tumors using different types of data, and to highlight supportive evidence for the proposed models. The exophytic part of primary and recurrence urothelial tumors were collected by cold-cup biopsy from patients undergoing transurethral resection at the Lund University Hospital, Sweden, between 2001 and 2007. In total, 49 tumors from 18 patients and their 18 matched normal samples obtained from peripheral blood were collected and hybridized on HumanCNV370-Duo Genotyping BeadChips (Illumina Inc.). Gene expression data were generated using Illumina HumanHT-12 Expression BeadChip. Tumors were classified according the Lund classification system. For 27 tumor samples and matched normal blood samples from 10 patients, a custom target captured panel was used to sequence 1697 cancer genes. We used the fact that patients with non-muscle invasive bladder tumors show frequent local recurrences and often have multiple tumors to study re-initiation of tumor growth from the same urothelium. By extensive genomic analyses we show that tumors from the same patient are clonal. We show that gross genomic chromosomal aberrations may be present then absent in a recurrent tumor. By analyses of incompatible changes i.e., genomic alterations that cannot be reversed, we show that almost all tumors from a single patient may show such changes, thus the tumors cannot have originated from each other. As recurring tumors share both genomic alterations and driver gene mutations these must have been present in the urothelium in periods with no overt tumor growth. The presence of similar mutational and CN profiles combined with incompatible events suggests that the primary and the recurrent tumors have a shared ancestry but are not originating from each other. This supports a model that includes a growing and evolving field of urothelial cells that occasionally, and locally, produce bursts of cellular growth leading to overt tumors.

Modulation of compatibility effects in response to experience: Two tests of initial and sequential learning.

Attentional control is a key component of goal-directed behavior. Modulation of this control in response to the statistics of the environment allows for flexible processing or suppression of relevant and irrelevant items in the environment. Modulation occurs robustly in compatibility-based attentional tasks, where incompatibility-related slowing is reduced when incompatible events are likely (i.e., the proportion compatibility effect; PCE). The PCE implicates dynamic changes in the measured compatibility effects that are central to fields of study such as attention, executive functions, and cognitive control. In these fields, stability in compatibility effects are generally assumed, which may be problematic if individual or group differences in measured compatibility effects may arise from differences in statistical learning speed or magnitude. Further, the sequential nature of many studies may lead the learning of certain statistics to be inadvertently applied to future behaviors. Here, we report tests of learning the PCE across conditions of task statistics and sequential blocks. We then test for the influence of feedback on the development of the PCE. We find clear evidence for the PCE, but no conclusive evidence for its slow development through experience. Initial experience with more incompatible trials selectively mitigated performance decreases in a subsequent block. Despite the lack of behavioral changes associated with patterns of learning, systematic within-task changes in compatibility effects remain an important possible source of variation in a wide range of attention research.

Bayesian assessment of the prevalence of <i>BRCA</i>-associated breast cancer in Moscow

Rationale: For many years, breast cancer has been leading in the cancer structure in women, accounting for 21% from the total number of newly diagnosed cases of malignancies in Russia. The literature on the prevalence of the BRCA-associated breast cancer is heterogeneous, which might be related to the specifics of the frequentist analysis. Aim: To assess the prevalence of BRCA-associated breast cancer and the probability of sporadic breast cancer in women of the Moscow region by Bayesian statistics. Materials and methods: The literature search in the E-library.ru database from January 2010 to March 2019 identified 13 original studies and 8 literature reviews with the data on hereditary breast cancer in the territories of the Russian Federation, Republic of Belarus and Ukraine. The assessment of the prevalence of BRCA gene mutation based on the Bayesian statistics and the full probability equation for incompatible events was performed on the data obtained in one study based on molecular genetic tests of 3826 female patients with breast cancer living in the Moscow Region, aged from 22 to 90 years (Russian Scientific Center of Roentgenoradiology). This was the most comprehensive study among those performed in Russia, covering almost all age ranges, with detailed description of the study design, diagnostic methods and the mutations spectrum analyzed. Results: The prevalence of BRCA1-associated breast cancer in Moscow among women is about 0.037%. The general population prevalence of the most frequent mutations of the BRCA1 gene (5382insC, 185delAG, 300T>G, 2080delA, 3819delGTAAA, 4153delA) in the female population in Moscow is about 0.05%, or about 0.1% from the total population. The probability of sporadic breast cancer in the female population of Moscow without any gene dominant mutations associated with breast cancer is about 1%. Conclusion: For the first time, the Bayesian statistics was used to analyze the prevalence of mutations in the BRCA1/2 genes in Russia. The results obtained are in good agreement with similar data for the Belgorod region and the Siberian region of Russian Federation, and the Grodno region of Belarus.

On quantum implication

Logic is an algebraic structure that defines a set of abstract rules which govern an area of interest. The abstraction property of the rules makes them reusable tools to model different problems and to reason with them. The proliferation of quantum theory brought attention to quantum logic which is a lattice of projectors and it is of importance to quantum computing. Unfortunately, basic tools like implication are not sufficiently studied in that logic, which prevents us from exploiting the power of quantum mechanics in reasoning. This note investigates the implication issue in quantum logic and defines a quantum implication operator for compatible events as well as for incompatible events. The suggested operator depends both on the angle between the vector sub-spaces of the involved events and the angles between the system state and the vector sub-spaces. It differentiates between three cases depending on the angle between the events’ sub-spaces. The article further shows through an example that some classical reasoning rules such as Modus Ponens and Modus Tollens hold given the suggested implication.

Метод расчета надежности невосстанавливаемых сложных по структуре систем, элементы которых могут находиться в трех несовместных состояниях

A method for estimating the reliability of structurally complex non-recoverable systems containing components that may exist in three incompatible states is developed based on the technique for decomposing systems having a complex structure of equivalent circuits with respect to the basic component and using the theorem about the sum of probabilities of incompatible events. By using the proposed method, it is possible to determine the probability that during a specified interval of time, there will be no random event as a result of which the link will become disconnected, or a through emergency short circuit fault current not cleared by current protection will flow between the input and output nodes of the electric power supply system equivalent circuit. An example of calculating the reliability of a complex system is given.

The Literary Work as a Semantic Amplifier

This article investigates the hermeneutic position of one text in relation to another one. More precisely, it is the case when one of the texts clarifies the meaning of another, amplifies the emphases of the other text, raises it to a higher power. A literary work with such explanatory intention is designated in the article with the term “semantic amplifier”. Its action is demonstrated by an analysis of two literary works of Dostoevsky: the novel “The Idiot” and the long short story “The Meek One”. The term “dissipative motif network” is introduced in order to designate a network of motifs, whose links stand significantly wide apart and refer to different narrative situations. The connections among the variants of the motifs are not obvious or graphic; they are so to speak dotted, implicit and require deciphering. In “The Idiot” the links of the motif network are such as marking oneself with a sign of the cross in front of an icon, deadly paleness, jumping, and blood. However, those are also the links of the motif chain that constitutes the suicide of the character in “The Meek One”. Nevertheless, when a reader goes through the lens of “The Idiot”, the linkage among these motifs in the long short story seems to be accelerated. What is separated in time and is indirectly connected, it becomes tightened and assembled. The dissipative motif network so to speak gathers up into one indivisible gesture in which this cause and effect merge together into one single trajectory of the jump, the end of which is the death of the character. It is as if what happens in “The Meek One” is latently set in advance in “The Idiot”. A jump from the stairs and a leaping from the roof are variants of the very important for Dostoevsky motif “threshold situation”, which is crossing the threshold in a literal and in a figurative sense; an act which marks a turning point in a plot when decisions are taken, characters go through a crisis and cross the border of incompatible events. When “The Meek One” is read in the sense of framework of “The Idiot”, the story has the function of a semantic amplifier: the jump from a low height turns into a jump from a great height; the almost unconscious ritual of bowing in front of the icon turns into jumping with an icon held in both hands, the deadly paleness understood figuratively turns into the real paleness of a dead body. Thus, in the process that is aimed at creating its artistic conception, a literary work enters into the depths of another literary work, deciphers its innermost messages, enunciates and articulates them with its own voice.

Herkansing voor infinitesimalen?

Abstract A New Chance for Infinitesimals? This article discusses the connection between the Zenonian paradox of magnitude and probability on infinite sample spaces. Two important premises in the Zenonian argument are: the Archimedean axiom, which excludes infinitesimal magnitudes, and perfect additivity. Standard probability theory uses real numbers that satisfy the Archimedean axiom, but it rejects perfect additivity. The additivity requirement for real-valued probabilities is limited to countably infinite collections of mutually incompatible events. A consequence of this is that there exists no standard probability function that describes a fair lottery on the natural numbers. If we reject the Archimedean axiom, allowing infinitesimal probability values, we can retain perfect additivity and describe a fair, countable infinite lottery. The article gives a historical overview to understand how the first option has become the current standard, whereas the latter remains ‘non-standard’.

PO-326 Genetic stability of multiple recurrences in bladder cancer patients

IntroductionTo describe the origin and the genetic relationship between primary bladder tumours and their recurrences, different models were proposed, such as, field cancerization, seeding, and intraepithelial migration. This study aims to investigate the genetic relationship in syn- and metachronous bladder tumours using different types of data, and to evaluate the proposed models.Material and methodsThe exophytic part of primary and recurrent urothelial tumours were collected by cold-cup biopsies from patients undergoing transurethral resection at the Lund University Hospital, Sweden, between 2001 and 2007. In total, 51 tumours from 19 patients and their 19 matched peripheral blood samples were collected and hybridised on Illumina HumanCNV370-Duo Genotyping array. Copy number data was extracted from GenomeStudio 2 software, and normalised using transformed quantile normalisation (tQN). Mirrored B allele frequency values were segmented using BAFsegmentation. Mutation calling was performed using targeted cancer gene sequencing panel. Gene expression data was generated using Illumina HumanHT-12 expression array.Results and discussionsA manual inspection of all copy number alterations (CNAs) profiles was performed. Normal cells content, tumour ploidy, and sub clonality were calculated, and the relationship between the primary and recurrent tumours were estimated. Preliminary results show that CNAs are early and stable events during the tumour evolution. Part of the syn- and metachronous bladder tumours shared similar mutational and CNAs profiles. However, even with similar profiles, some events such as loss of heterozygosity in the primary tumours, were not observed in the recurrent tumours, constituting incompatible events. Samples with mutations in TP53 or amplification in MDM2 showed higher number of break points in the genome. A further analysis will be performed using the available CNAs, expression, and mutational data.ConclusionThe genetic relationship in syn- and metachronous bladder tumours was investigated using different data types providing a better understanding of bladder cancer evolution. The presence of similar mutational and CNAs profiles combined with incompatible events suggests that the primary and the recurrent tumours were generated separately from a common ancestor. These findings highlight a tumour evolution scenario of a clonal cancerized field.

Seismic rehabilitation effect in a steel moment frame subjected to tow critical loads

PurposeThe purpose of this paper is to present a probabilistic assessment and verify the effectiveness of seismic improvement schemes against earthquake, blast and progressive collapse. The probabilistic analysis is performed by taking into account the uncertainties in loading such as planar configuration and amplitude of the blast loading. A standard Monte Carlo (MC) simulation method is employed to generate various concepts of the uncertain parameters within the problem. For a given concept, various local dynamic analyses are performed within a certain range of distance, in order to quantify and locate the damage induced by impact wave on structural elements. In the next step, a limit state analysis is performed in order to investigate whether a progressive collapse mechanism forms under the acting loads or not.Design/methodology/approach( | ) and ( | ) are blast fragility and seismic fragility, respectively; ( ) and ( ) are annual occurrence rate of earthquake and blast, respectively. The purpose of the current study is to calculate for the primary structure as well as the retrofitted structure. Annual occurrence rate of earthquake can be calculated by using probability seismic hazard analysis for the site of interest, where the structure is located. In this paper, blast fragility and seismic fragility are defined rather differently; in other words, seismic fragility is defined as the probability of structural collapse given a specified level of seismic intensity whereas blast fragility is defined as the probability of collapse given that a significant blast event takes place. Both blast and earthquake loading conditions involve the activation of energy dissipation mechanism and, as a consequence, both can be resisted employing ductility enhancing techniques, such as column wrapping or jacketing and steel bracing.FindingsThe current paper aims to present a probabilistic assessment of progressive collapse under blast and earthquake loads. Non-dependent and incompatible events are considered to obtain a general rate of collapse. Finally, probabilistic collapse rate was obtained for a moment frame before and after modifying with convergent steel brace (CBF). The purpose of doing so is to investigate whether seismic improvement schemes can reduce collapse risk of different critical events or not.Originality/valueObjective of the present work is to present a methodology for calculating the annual risk of collapse for a civil structure subjected to both seismic and blast loads, using a bi-hazard approach. Given that a blast event takes place, the probability of progressive collapse is calculated using a MC simulation procedure. The simulation procedure implements an efficient non-linear limit state analysis, formulated and solved as a linear programming problem. The probability of collapse caused by an earthquake event can be calculated by integrating the seismic fragility of the structure and the seismic hazard for the site.

Branching with Uncertain Semantics

Branching with Uncertain Semantics

Non‐antagonistic relationship between mitogenic factors and cAMP in adult Schwann cell re‐differentiation

The expression of myelination-associated genes (MGs) can be induced by cyclic adenosine monophosphate (cAMP) elevation in isolated Schwann cells (SCs). To further understand the effect of known SC mitogens in the regulation of SC differentiation, we studied the response of SCs isolated from adult nerves to combined cAMP, growth factors, including neuregulin, and serum. In adult SCs, the induction of MGs by cAMP coincided with the loss of genes expressed in non-myelin-forming SCs and with a change in cell morphology from a bipolar to an expanded epithelial-like shape. Prolonged treatment with high doses of cAMP-stimulating agents, as well as low cell density, was required for the induction of SC differentiation. Stimulation with serum, neuregulin alone, or other growth factors including PDGF, IGF and FGF, increased SC proliferation but did not induce the expression of MGs or the associated morphological change. Most importantly, when these factors were administered in combination with cAMP-stimulating agents, SC proliferation was synergistically increased without reducing the differentiating activity of cAMP. Even though the initiation of DNA synthesis and the induction of differentiation were mostly incompatible events in individual cells, SCs were able to differentiate under conditions that also supported active proliferation. Overall, the results indicate that in the absence of neurons, cAMP can trigger SC re-differentiation concurrently with, but independently of, growth factor signaling.

A comparison of two‐particle models for conduction electron scattering on hydrogen‐like impurity ions in non‐degenerate semiconductors

AbstractModels of electron mobility limited by scattering of conduction electrons on hydrogen‐like impurity ions in non‐degenerate crystalline semiconductors are discussed. It is shown that the best agreement with experimental data is given by a model earlier proposed by the authors, in which the time of electron‐ion interaction, equal to the time of transfer of a conduction electron across a spherical region corresponding to one impurity ion in the crystal, is taken into account, the minimum scattering angle is chosen according to Conwell–Weisskopf, and scattering acts of an electron on impurity ions are considered independent and incompatible events. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Research on Logical-and-Probabilistic Modeling of Security Portfolio and Copulas

The technique of application of copulas in modeling of security portfolios by logical-and-probabilistic theory with groups of incompatible events is suggested. Results of analysis with two types of copulas are presented. The effectivesness of combination of logical-and-probabilistic theory and copulas is proved.

On Relations Between Probabilities Under Quantum and Classical Measurements

We show that the so-called quantum probabilistic rule, usually presented in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is usually considered, in contrast to the rule for the addition of probabilities of incompatible events. The latter is, of course, valid under all measurement situations upon classical and quantum objects. We discuss also quantum measurement situation, which is similar to the classical one, corresponding to classical Bayes' formula for conditional probabilities. We show the compatibility of description of this quantum measurement situation in the frame of purely classical and experimentally justified straight ward frequency arguments [Khrennikov (1999, 2000, 2001)] and in the frame of the quantum stochastic approach to the description of generalized quantum measurements (Loubenets (2000); Barndorff-Nielsen and Loubenets (2001)]. In view of derived results, we argue that even in the classical probability the classical Bayes' formula describes a particular case of the considered measurement situation, which is specific for context-independent measurements. The similarity of the forms of the relation between the transformation of probabilities, which we derive in the frame of quantum stochastic approach and in the frame of straight ward frequency arguments, underlines once more that the projective (von Neumann) measurements correspond only to a very special kind of measurement situations in quantum theory.

A semiclassical approach to Coulomb scattering of conduction electrons on ionized impurities in nondegenerate semiconductors

In the proposed model of mobility, the time of electron–ion interaction equals the time taken by the conduction electron to pass a spherical region, corresponding to one impurity ion in crystal, and the minimum scattering angle is determined after Conwell–Weisskopf. We consider the acts of electron scattering on ions as independent and incompatible events. It is shown in the approximation of quasimomentum relaxation time, that for nondegenerate semiconductors, the mobility μi, limited by the elastic scattering by impurity ions with the concentration Ni, is proportional to T/Ni2/3; the Hall factor equals 1.4. The calculated dependences of the mobility of the majority charge carriers upon their concentration for different temperatures T agree well with known experimental data. It is shown, that the Brooks–Herring formula μBH∝T3/2/Ni gives overestimated values of mobility. Comparison of the calculations of mobility in degenerate semiconductors with experimental data also yields μi<μBH.