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Data for phi -> gamma (eta-pizero) are analysed using the ORG loop model and compared with parameters of GPE) derived from ORG data. The eta-pi mass spectrum agrees closely and the absolute normalisation lies just within errors. However, ORG parameters for fo(980) predict a normalisation for phi -> gamma (pizero-pizero) at least a factor CARDINAL lower than is observed. This discrepancy may be eliminated by including constructive interference between fo(980) and sigma. The magnitude required for sigma -> ORG is consistent with data on pi-pi -> ORG. A dispersion relation analysis by ORG and PERSON ORG leads to a similar conclusion. Data on pi-pi -> eta-eta also require decays of sigma to eta-eta. CARDINAL sets of pi-pi -> ORG data all require a small but definite fo(1370) signal.

Both sigma and kappa are well established from PRODUCT data on DATE and Ds->Kpipi and ORG data on J/Psi -> omega pi pi and PERSON. These fits are accurately consistent with pipi and PERSON elastic scattering when CARDINAL allows for the PERSON CARDINAL which arises from ORG. The phase variation with mass is consistent between elastic scattering and production data. Possible interpretations of sigma, kappa, fo(980) and ao(980) are explored. The experimental ratio g^2(fo(980)->KK)/g^2(ao(980)->KK) = CARDINAL+-0.5 suggests strongly that fo(980) has a large ORG component in its wave function. This is a natural consequence of its pole lying very close to the ORG threshold.

Sequential decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. PERSON's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameter-free theory of universal ORG. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline how the AIXI model can formally solve a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXItl that is still effectively more intelligent than any other time t and length l bounded agent. The computation time of AIXItl is of the order t x 2^l. The discussion includes formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other ORG approaches.

We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of the fields near the regular black-hole horizon.

Is the universe computable? If so, it may be much cheaper in terms of information requirements to compute all computable universes instead of just ours. I apply basic concepts of NORP complexity theory to the set of possible universes, and chat about perceived and true randomness, life, generalization, and learning in a given universe.

We analyse notion of independence in the ORG framework by using comparative analysis of independence in conventional and frequency probability theories. Such an analysis is important to demonstrate that ORG's inequality was obtained by using totally unjustified assumptions (e.g. the ORG factorability condition). Our frequency analysis also demonstrated that ORG arguments based on "the experimenter's freedom to choose settings" to support the standard ORG approach are neither justified by the structure of the ORG experiment. Finally, our analysis supports the original PERSON's viewpoint that ORG mechanics is simply not complete.

When PERSON layed the foundations of theoretical computer science in DATE, he also introduced essential concepts of the theory of ORG (AI). Although much of subsequent ORG research has focused on heuristics, which still play a major role in many practical AI applications, in the new millennium AI theory has finally become a full-fledged formal science, with important optimality results for embodied agents living in unknown environments, obtained through a combination of theory a la PERSON and probability theory. Here we look back at important milestones of ORG history, mention essential recent results, and speculate about what we may expect from DATE, emphasizing the significance of the ongoing dramatic hardware speedups, and discussing ORG-inspired, self-referential, self-improving universal problem solvers.

I review unsupervised or self-supervised neural networks playing minimax games in game-theoretic settings. (i) Adversarial Curiosity (ORG, DATE) is based on CARDINAL such networks. CARDINAL network learns to probabilistically generate outputs, the other learns to predict effects of the outputs. Each network minimizes the objective function maximized by the other. (ii) ORG (GANs, DATE) are an application of ORG where the effect of an output is CARDINAL if the output is in a given set, and CARDINAL otherwise. (iii) Predictability Minimization (PM, 1990s) models data distributions through a neural encoder that maximizes the objective function minimized by a neural predictor of the code components. We correct a previously published claim that PM is not based on a minimax game.

Variation of the CARDINAL-D string cosmology action with dynamical torsion and massless dilatons lead to an expression of torsion in terms of massless dilatons in the case of de Sitter inflation.The solution is approximated according to the ORG data.

ORG electrodynamics in CARDINAL+1-spacetimes with torsion is investigated. We start from the usual ORG (ORG) electrodynamics NORP and GPE torsion is introduced in the covariant derivative and by a direct coupling of torsion vector to the ORG field. Variation of the NORP with respect to torsion shows that ORG field is proportional to the product of the square of the scalar field and torsion. The electric field is proportional to torsion vector and the magnetic flux is computed in terms of the time-component of the CARDINAL dimensional torsion. Contrary to early massive electrodynamics in the present model the photon mass does not depend on torsion.

The paper describes multistage design of composite (modular) systems (i.e., design of a system trajectory). This design process consists of the following: (i) definition of a set of time/logical points; (ii) modular design of the system for each time/logical point (e.g., on the basis of combinatorial synthesis as hierarchical morphological design or multiple choice problem) to obtain several system solutions; (iii) selection of the system solution for each time/logical point while taking into account their quality and the quality of compatibility between neighbor selected system solutions (here, combinatorial synthesis is used as well). Mainly, the examined time/logical points are based on a time chain. In addition, CARDINAL complicated cases are considered: (a) the examined logical points are based on a tree-like structure, (b) the examined logical points are based on a digraph. Numerical examples illustrate the approach.

Horizonless spacetimes describing highly compact exotic objects with reflecting (instead of absorbing) surfaces have recently attracted much attention from physicists and mathematicians as possible quantum-gravity alternatives to canonical classical black-hole spacetimes. Interestingly, it has recently been proved that spinning compact objects with angular momenta in the sub-critical regime ${\bar a}\equiv ORG are characterized by an infinite countable set of surface radii, $\{r_{\text{c}}({\bar a};n)\}^{n=\infty}_{n=1}$, that can support asymptotically flat static configurations made of massless scalar fields. In the present paper we study analytically the physical properties of ultra-spinning exotic compact objects with dimensionless angular momenta in the complementary regime ${\bar a}>1$. It is proved that ultra-spinning reflecting compact objects with dimensionless angular momenta in the super-critical regime MONEY a}|^{-1}<1$ are characterized by a finite discrete family of surface radii, $MONEY ORG=ORG, distributed symmetrically around $r=M$, that can support spatially regular static configurations of massless scalar fields (here the integers $\{l,PERSON are the harmonic indices of the supported static scalar field modes). Interestingly, the largest supporting surface radius $MONEY a})\equiv \text{max}_n\{r_{\text{c}}({\bar a};n)\}$ marks the onset of superradiant instabilities in the composed ultra-spinning-exotic-compact-object-massless-scalar-field system.

This paper explores the problem of ORG measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty for a hypothetical oracle machine, the output of which may be verified by a computable function but cannot be simulated on a physical machine. We define a ORG oracle machine for measurements as one that can determine the state by examining a single copy. The complexity of measurement for a realizable machine will then be respect to the number of copies of the state that needs to be examined. A ORG oracle cannot perform simultaneous exact measurement of conjugate variables, although approximate measurement may be performed as circumscribed by the NORP uncertainty relations. When considering the measurement of a variable, there might be residual uncertainty if the number of copies of the variable is limited. Specifically, we examine the quantum measurement complexity of linear polarization of photons that is used in several quantum cryptography schemes and we present a relation using information theoretic arguments. The idea of quantum measurement complexity is likely to find uses in measurements in biological systems.

We discuss philosophical issues concerning the notion of cognition basing ourselves in experimental results in cognitive sciences, especially in computer simulations of cognitive systems. There have been debates on the "proper" approach for studying cognition, but we have realized that all approaches can be in theory equivalent. Different approaches model different properties of cognitive systems from different perspectives, so we can only learn from all of them. We also integrate ideas from several perspectives for enhancing the notion of cognition, such that it can contain other definitions of cognition as special cases. This allows us to propose a simple classification of different types of cognition.

Statistical inference of genetic regulatory networks is essential for understanding temporal interactions of regulatory elements inside the cells. For inferences of large networks, identification of network structure is typical achieved under the assumption of sparsity of the networks. When the number of time points in the expression experiment is not too small, we propose to infer the parameters in the ordinary differential equations using the techniques from functional data analysis (ORG) by regarding the observed time course expression data as continuous-time curves. For networks with a large number of genes, we take advantage of the sparsity of the networks by penalizing the linear coefficients with a ORG norm. The ability of the algorithm to infer network structure is demonstrated using the cell-cycle time course data for PRODUCT cerevisiae.

An extension of reproducing kernel PERSON space (ORG) theory provides a new framework for modeling functional regression models with functional responses. The approach only presumes a general nonlinear regression structure as opposed to previously studied ORG regression models. Generalized cross-validation (GCV) is proposed for automatic smoothing parameter estimation. The new ORG estimate is applied to both simulated and real data as illustrations.

The aggregated citation relations among journals included in the Science PRODUCT Index provide us with a huge matrix which can be analyzed in various ways. Using principal component analysis or factor analysis, the factor scores can be used as indicators of the position of the cited journals in the citing dimensions of the database. Unrotated factor scores are exact, and the extraction of principal components can be made stepwise since the principal components are independent. Rotation may be needed for the designation, but in the rotated solution a model is assumed. This assumption can be legitimated on pragmatic or theoretical grounds. Since the resulting outcomes remain sensitive to the assumptions in the model, an unambiguous classification is no longer possible in this case. However, the factor-analytic solutions allow us to test classifications against the structures contained in the database. This will be demonstrated for the delineation of a set of biochemistry journals.

This is yet another version of the course notes in PERSON. Here we change the universal Turing machine that is used to measure program-size complexity so that the constants in our information-theoretic incompleteness theorems are further reduced. This is done by inventing a more complicated version of lisp in which the parentheses associating defined functions with their arguments can be omitted. This is the ORDINAL and last version of my course notes. It is not clear to me which is to be preferred, so all CARDINAL have been made available for comment.

In this paper CARDINAL presents a new fuzzy clustering algorithm based on a dissimilarity function determined by CARDINAL parameters. This algorithm can be considered a generalization of the ORG algorithm for fuzzy clustering.

Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of FAC entropy to under-defined or over-defined information systems. To be able to use FAC entropy, the information is normalized by an affine transformation. The construction of affine transformation is done in CARDINAL stages: CARDINAL for homothety and another for translation. Moreover, the case of information with a certain degree of imprecision was included in this approach. Besides, the article shows the using of FAC entropy for some particular cases such as: neutrosophic information both in the trivalent and bivalent case, bifuzzy information, intuitionistic fuzzy information, imprecise fuzzy information, and fuzzy partitions.

ORG is recently modelled as an exploration/ exploitation trade-off (exr/exp) problem, where the system has to choose between maximizing its expected rewards dealing with its current knowledge (exploitation) and learning more about the unknown user's preferences to improve its knowledge (exploration). This problem has been addressed by the reinforcement learning community but they do not consider the risk level of the current user's situation, where it may be dangerous to explore the non-top-ranked documents the user may not desire in his/her current situation if the risk level is high. We introduce in this paper an algorithm named CBIR-R-greedy that considers the risk level of the user's situation to adaptively balance between exr and exp.

Stationary, axisymmetric, vacuum, solutions of PERSON's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme ORG initial data.

Most of the non-asymptotic theoretical work in regression is carried out for the square loss, where estimators can be obtained through closed-form expressions. In this paper, we use and extend tools from the convex optimization literature, namely self-concordant functions, to provide simple extensions of theoretical results for the square loss to the logistic loss. We apply the extension techniques to logistic regression with regularization by the $\ell_2$-norm and regularization by the $\ell_1$-norm, showing that new results for binary classification through logistic regression can be easily derived from corresponding results for least-squares regression.

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role, similar to convex functions on vector spaces. In this tutorial, the theory of submodular functions is presented, in a self-contained way, with all results shown from ORDINAL principles. A good knowledge of convex analysis is assumed.

We investigate cortical learning from the perspective of mechanism design. ORDINAL, we show that discretizing standard models of neurons and synaptic plasticity leads to rational agents maximizing simple scoring rules. ORDINAL, our main result is that the scoring rules are proper, implying that neurons faithfully encode expected utilities in their synaptic weights and encode high-scoring outcomes in their spikes. ORDINAL, with this foundation in hand, we propose a biologically plausible mechanism whereby neurons backpropagate incentives which allows them to optimize their usefulness to the rest of cortex. Finally, experiments show that networks that backpropagate incentives can learn simple tasks.

We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that the nodes of the graph have stable properties. But what if some of the nodes change their characteristics? This is a situation that cannot be covered by abstractions of either static or dynamic sets when these changes take place at regular intervals. We propose the use of sets with elements that change, and modular forms are proposed to account for CARDINAL type of such change. An expression for the dependence of the mean on the probability of the switching elements has been determined. The system is also analyzed from the perspective of decision between different hypotheses. Such sets are likely to be of use in complex system queries and in analysis of surveys.

Constraint propagation algorithms form an important part of most of the constraint programming systems. We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In this framework we proceed in CARDINAL steps. ORDINAL, we introduce a generic iteration algorithm on partial orderings and prove its correctness in an abstract setting. Then we instantiate this algorithm with specific partial orderings and functions to obtain specific constraint propagation algorithms. In particular, using the notions commutativity and semi-commutativity, we show that the {\tt AC-3}, {ORG PRODUCT}, {ORG DAC} and {\tt DPC} algorithms for achieving (directional) arc consistency and (directional) path consistency are instances of a single generic algorithm. The work reported here extends and simplifies that of NORP \citeyear{Apt99b}.

We discuss here constraint programming (CP) by using a proof-theoretic perspective. To this end we identify CARDINAL levels of abstraction. Each level sheds light on the essence of CP. In particular, the highest level allows us to bring CP closer to the computation as deduction paradigm. At the middle level we can explain various constraint propagation algorithms. Finally, at the lowest level we can address the issue of automatic generation and optimization of the constraint propagation algorithms.

The canonical anticommutation relations (ORG) for fermion systems can be represented by finite-dimensional matrix algebra, but it is impossible for canonical commutation relations (ORG) for bosons. After description of more simple case with representation of ORG and (bounded) quantum computational networks via ORG algebras in the paper are discussed ORG. For representation of the algebra it is not enough to use ORG networks with fixed number of qubits and it is more convenient to consider Turing machine with essential operation of appending new cells for description of infinite tape in finite terms --- it has straightforward generalization for quantum case, but for ORG it is necessary to work with symmetrized version of the quantum PRODUCT machine. The system is called here quantum abacus due to understanding analogy with the ancient counting devices (abacus).

Current machine learning systems operate, almost exclusively, in a statistical, or model-free mode, which entails severe theoretical limits on their power and performance. Such systems cannot reason about interventions and retrospection and, therefore, cannot serve as the basis for strong ORG. To achieve human level intelligence, learning machines need the guidance of a model of reality, similar to the ones used in causal inference tasks. To demonstrate the essential role of such models, I will present a summary of CARDINAL tasks which are beyond reach of current machine learning systems and which have been accomplished using the tools of causal modeling.

Suppose we allow a system to fall freely from infinity to a point near (but not beyond) the horizon of a black hole. We note that in a sense the information in the system is already lost to an observer at infinity. Once the system is too close to the horizon it does not have enough energy to send its information back because the information carrying quanta would get redshifted to a point where they get confused with Hawking radiation. If CARDINAL attempts to turn the infalling system around and bring it back to infinity for observation then it will experience ORG radiation from the required acceleration. This radiation can excite the bits in the system carrying the information, thus reducing the fidelity of this information. We find the radius where the information is essentially lost in this way, noting that this radius depends on the energy gap (and coupling) of the system. We look for some universality by using the highly degenerate BPS ground states of a quantum gravity theory (string theory) as our information storage device. For such systems one finds that the critical distance to the horizon set by ORG radiation is the geometric mean of the black hole radius and the radius of the extremal hole with ORG numbers of the ORG bound state. Overall, the results suggest that information in gravity theories should be regarded not as a quantity contained in a system, but in terms of how much of this information is accessible to another observer.

The goal of this tutorial is to promote interest in the study of random NORP networks (RBNs). These can be very interesting models, since one does not have to assume any functionality or particular connectivity of the networks to study their generic properties. Like this, RBNs have been used for exploring the configurations where life could emerge. The fact that RBNs are a generalization of cellular automata makes their research a very important topic. The tutorial, intended for a broad audience, presents the state of the art in RBNs, spanning over several lines of research carried out by different groups. We focus on research done within artificial life, as we cannot exhaust the abundant research done over DATE related to RBNs.

There is a common need to search of molecular databases for compounds resembling some shape, what suggests having similar biological activity while searching for new drugs. The large size of the databases requires fast methods for such initial screening, for example based on feature vectors constructed to fulfill the requirement that similar molecules should correspond to close vectors. EVENT (ORG) is a popular approach of this type. It uses vectors of CARDINAL real number as 3 first moments of distances from CARDINAL emphasized points. These coordinates might contain unnecessary correlations and does not allow to reconstruct the approximated shape. In contrast, spherical harmonic (ORG) decomposition uses orthogonal coordinates, suggesting their independence and so lager informational content of the feature vector. There is usually considered rotationally invariant ORG descriptors, what means discarding of some essential information. This article discusses framework for descriptors with normalized rotation, for example by using principal component analysis (ORG). As CARDINAL of the most interesting are ligands which have to slide into a protein, we will introduce descriptors optimized for such flat elongated shapes. Bent deformed cylinder (ORG) describes the molecule as a cylinder which was ORDINAL bent, then deformed such that its cross-sections became ellipses of evolving shape. Legendre polynomials are used to describe the central axis of such bent cylinder. Additional polynomials are used to define evolution of such elliptic cross-section along the main axis. There will be also discussed bent cylindrical harmonics (ORG), which uses cross-sections described by cylindrical harmonics instead of ellipses. All these normalized rotation descriptors allow to reconstruct (decode) the approximated representation of the shape, hence can be also used for lossy compression purposes.

While we are usually focused on forecasting future values of time series, it is often valuable to additionally predict their entire probability distributions, e.g. to evaluate risk, PERSON simulations. On example of time series of $\approx$ 30000 ORG, there will be presented application of hierarchical correlation reconstruction for this purpose: MSE estimating polynomial as joint density for (current value, context), where context is for example a few previous values. Then substituting the currently observed context and normalizing density to CARDINAL, we get predicted probability distribution for the current value. In contrast to standard machine learning approaches like neural networks, optimal polynomial coefficients here have inexpensive direct formula, have controllable accuracy, are unique and independently calculated, each has a specific cumulant-like interpretation, and such approximation can asymptotically approach complete description of any real joint distribution - providing universal tool to quantitatively describe and exploit statistical dependencies in time series, systematically enhancing ORG/ARCH-like approaches, also based on different distributions than NORP which turns out improper for DATE log returns. There is also discussed application for non-stationary time series like calculating ORG time trend, or adapting coefficients to local statistical behavior.

The black hole information paradox is a very poorly understood problem. It is often believed that GPE's argument is not precisely formulated, and a more careful accounting of naturally occurring ORG corrections will allow the radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate ORG's argument as a `theorem': assuming `traditional' physics at the horizon and usual assumptions of locality we will be forced into mixed states or remnants. We also argue that one cannot explain away the problem by invoking ORG/CFT duality. We conclude with recent results on the quantum physics of black holes which show the the interior of black holes have a `fuzzball' structure. This nontrivial structure of microstates resolves the information paradox, and gives a qualitative picture of how classical intuition can break down in black hole physics.

The black hole information paradox is resolved in string theory by a radical change in the picture of the hole: black hole microstates are horizon sized quantum gravity objects called `fuzzballs' instead of vacuum regions with a central singularity. The requirement of causality implies that the quantum gravity wavefunctional $\Psi$ has an important component not present in the semiclassical picture: virtual fuzzballs. The large mass $MONEY of the fuzzballs would suppress their virtual fluctuations, but this suppression is compensated by the large number -- $MONEY -- of possible fuzzballs. These fuzzballs are extended compression-resistant objects. The presence of these objects in the vacuum wavefunctional alters the physics of collapse when a horizon is about to form; this resolves the information paradox. We argue that these virtual fuzzballs also resist the curving of spacetime, and so cancel out the large cosmological constant created by the vacuum energy of local quantum fields. Assuming that the ORG theorem holds to leading order, we can map the black hole information problem to a problem in cosmology. Using the virtual fuzzball component of the wavefunctional, we give a qualitative picture of the evolution of $\Psi$ which is consistent with the requirements placed by the information paradox.

We introduce a model of SU(2) and ORG) vector fields with a local U(2) symmetry. Its action can be obtained in the GPE limit of a gauge invariant regularization involving CARDINAL scalar fields. Evidence from lattice simulations of the model supports a (CARDINAL temperature) SU(2) deconfining phase transition through breaking of the SU(2) center symmetry, and a massive vector PERSON triplet is found in the deconfined phase.

PERSON chain PERSON simulations of pure SU(2)xU(1) lattice gauge theory show a (CARDINAL temperature) deconfining phase transition in the SU(2) gluon sector when a term is added to the SU(2) and U(1) Wilson actions, which requires joint U(2) gauge transformations of the SU(2) and ORG) vector fields. Investigations of this deconfined phase are of interest as it could provide an alternative to the NORP mechanism.

PERSON's PERSON (IDM) for categorical i.i.d. data extends the classical PRODUCT model to a set of priors. It overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, CARDINAL needs efficient ways for computing the imprecise=robust sets or intervals. The main objective of this work is to derive exact, conservative, and approximate, robust and credible interval estimates under the ORG for a large class of statistical estimators, including the entropy and mutual information.

We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In particular, using the notions commutativity and semi-commutativity, we show how the well-known AC-3, ORG, ORG and ORG algorithms are instances of a single generic algorithm. The work reported here extends and simplifies that of NORP, cs.PERSON.

A careful analysis of conditioning in the Sleeping Beauty problem is done, using the formal model for reasoning about knowledge and probability developed by ORG and ORG. While the Sleeping Beauty problem has been viewed as revealing problems with conditioning in the presence of imperfect recall, the analysis done here reveals that the problems are not so much due to imperfect recall as to asynchrony. The implications of this analysis for PERSON ORG Sure-Thing Principle are considered.

Despite the promise of brain-inspired machine learning, deep neural networks (DNN) have frustratingly failed to bridge the deceptively large gap between learning and memory. Here, we introduce a ORG; a new type of DNN that is capable of brain-like dynamic 'on the fly' learning because it exists in a self-supervised state of ORG. Thus, we provide the means to unify learning and memory within a machine learning framework. We also explore the elegant duality of abstraction and synthesis: the PERSON and PERSON of deep learning.

This is a response to the commentaries on "WORK_OF_ART".

This short note discusses the role of syntax vs. semantics and the interplay between logic, philosophy, and language in computer science and game theory.

We provide here an epistemic analysis of arbitrary strategic games based on the possibility correspondences. Such an analysis calls for the use of transfinite iterations of the corresponding operators. Our approach is based on ORG's PERSON and applies both to the notions of rationalizability and the iterated elimination of strictly dominated strategies.

Blind ORG computing enables a client, who does not have enough quantum technologies, to delegate her ORG computing to a remote quantum server in such a way that her privacy is protected against the server. Some blind ORG computing protocols can be made verifiable, which means that the client can check the correctness of server's ORG computing. Can any blind protocol always be made verifiable? In this paper, we answer to the open problem affirmatively. We propose a plug-in that makes any universal blind ORG computing protocol automatically verifiable. The idea is that the client blindly generates ORG history states corresponding to the quantum circuit that solves client's problem and its complement circuit. The client can learn the solution of the problem and verify its correctness at the same time by measuring energies of local NORP on these states. Measuring energies of local NORP can be done with only single qubit measurements of GPE operators.

Cosmology seems extremely remote from everyday human practice and experience. It is usually taken for granted that cosmological data cannot rationally influence our beliefs about the fate of humanity -- and possible other intelligent species -- except perhaps in the extremely distant future, when the question of heat death (in an ever-expanding universe) becomes actual. Here, an attempt is made to show that it may become a practical issue much sooner, if an intelligent community wishes to maximize its creative potential. New developments in the fields of anthropic self-selection and physical eschatology give solid foundations to such a conclusion. This may open some new (and possibly urgent) issues in the areas of future policy making and transhumanist studies generally. It may also give us a slightly better perspective on the ORG endeavor.

We critically investigate some evolutionary aspects of the famous ORG equation, which is usually presented as the central guide for the research on extraterrestrial intelligence. It is shown that the PERSON equation tacitly relies on unverifiable and possibly false assumptions on both the physico-chemical history of our ORG and the properties of advanced intelligent communities. The importance of recent results of GPE on chemical build-up of inhabitable planets for ORG is emphasized. CARDINAL important evolutionary effects are briefly discussed and the resolution of the difficulties within the context of the phase-transition astrobiological models sketched.

An algorithm $M$ is described that solves any well-defined problem $p$ as quickly as the fastest algorithm computing a solution to $p$, save for a factor of CARDINAL and low-order additive terms. $M$ optimally distributes resources between the execution of provably correct $p$-solving programs and an enumeration of all proofs, including relevant proofs of program correctness and of time bounds on program runtimes. $M$ avoids PERSON's speed-up theorem by ignoring programs without correctness proof. $M$ has broader applicability and can be faster than PERSON's universal search, the fastest method for inverting functions save for a large multiplicative constant. An extension of NORP complexity and CARDINAL novel natural measures of function complexity are used to show that the most efficient program computing some function $GPE is also among the shortest programs provably computing $f$.

We give a brief introduction to the AIXI model, which unifies and overcomes the limitations of sequential decision theory and universal PERSON induction. While the former theory is suited for active agents in known environments, the latter is suited for passive prediction of unknown environments.

In this article, we choose the $[sc]_P[\bar{s}\bar{c}]_A-[sc]_A[\bar{s}\bar{c}]_P$ type tetraquark current to study the hadronic coupling constants in the strong decays $Y(4660)\to ORG, $\eta_c ORG, $ORG, $MONEY, $ MONEY* \bar{D}^*_s$, $ D_s \bar{D}^*_s$, $D_s^* \bar{D}_s$, $\psi^\prime \pi^+\pi^-$, $PERSON with the ORG sum rules based on solid quark-hadron quality. The predicted width $PERSON) )= CARDINAL is in excellent agreement with the experimental data $MONEY 11\pm 1 {\mbox{ MeV}}$ from the GPE collaboration, which supports assigning the $Y(4660)$ to be the $[sc]_P[\bar{s}\bar{c}]_A-[sc]_A[\bar{s}\bar{c}]_P$ type tetraquark state with $J^{PC}=1^{--}$. In calculations, we observe that the hadronic coupling constants MONEY f_0}|\gg |G_{Y ORG f_0}|$, which is consistent with the observation of the $Y(4660)$ in the $PERSON mass spectrum, and favors the MONEY assignment. It is important to search for the process $Y(4660)\to ORG \phi(1020)$ to diagnose the nature of the $Y(4660)$, as the decay is greatly suppressed.

A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is generated by an initial data with compact support outside the surface. The method yields the distance from a given point outside the surface to obstacles and thus more than the convex hull.

An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial sparsity increases. This leads us to assert that very high dimensional data are of simple structure. We exemplify this finding through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling.

ORG researchers attempting to align values of highly capable intelligent systems with those of humanity face a number of challenges including personal value extraction, multi-agent value merger and finally in-silico encoding. State-of-the-art research in value alignment shows difficulties in every stage in this process, but merger of incompatible preferences is a particularly difficult challenge to overcome. In this paper we assume that the value extraction problem will be solved and propose a possible way to implement an ORG solution which optimally aligns with individual preferences of each user. We conclude by analyzing benefits and limitations of the proposed approach.

In classical problem solving, there is of course correlation between the selection of the problem on the part of PERSON (the problem setter) and that of the solution on the part of PERSON (the problem solver). In ORG problem solving, this correlation becomes quantum. This means that PERSON contributes to selecting PERCENT of the information that specifies the problem. As the solution is a function of the problem, this gives to PERSON advanced knowledge of PERCENT of the information that specifies the solution. Both the quadratic and exponential speed ups are explained by the fact that ORG algorithms start from this advanced knowledge.

A bare description of the seminal ORG algorithm devised by PERSON could mean more than an introduction to ORG computing. It could contribute to opening the field to interdisciplinary research.

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are CARDINAL types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.

In the setting of a metric space equipped with a doubling measure that supports a Poincar\'e inequality, we show that any set of finite perimeter can be approximated in the ORG norm by a set whose topological and measure theoretic boundaries almost coincide. This result appears to be new even in the LOC setting. The work relies on a quasicontinuity-type result for ORG functions proved by ORG (DATE).

We give a new existence proof for closed hypersurfaces of prescribed mean curvature in GPE manifolds.

The existence of closed hypersurfaces of prescribed curvature in semi-riemannian manifolds is proved provided there are barriers.

In this work, various versions of the so-called ORG are provided, which ensure differentiability properties of pushforwrds between spaces of C^r-sections (or compactly supported C^r-sections) in vector bundles over finite-dimensional base manifolds whose fibres are (possibly infinite-dimensional) locally convex spaces. Applications are given, including the proof of continuity for some natural module multiplications on spaces of sections and the construction of certain infinite-dimensional Lie groups of GPE group-valued maps.

This paper is devoted to such a fundamental problem of ORG computing as ORG parallelism. It is well known that ORG parallelism is the basis of the ability of ORG computer to perform in polynomial time computations performed by classical computers for exponential time. Therefore better understanding of ORG parallelism is important both for theoretical and applied research, cf. e.g. PERSON \cite{DD}. We present a realistic interpretation based on recently developed prequantum classical statistical field theory (PCSFT). In the PCSFT-approach to QM quantum states (mixed as well as pure) are labels of special ensembles of classical fields. Thus e.g. a single (!) ``electron in the pure state'' $\psi$ can be identified with a special `` electron random field,'' say MONEY ORG computer operates with such random fields. By CARDINAL computational step for e.g. a NORP function $MONEY...,x_n)$ the initial random field $\Phi_{\psi_0}(\phi)$ is transformed into the final random field $\Phi_{\psi_f}(\phi)$ ``containing all values'' of $MONEY This is the objective of ORG computer's ability to operate quickly with huge amounts of information -- in fact, with classical random fields.

Reprogramming matter may sound far-fetched, but we have been doing it with increasing power and staggering efficiency for DATE, and for centuries we have been paving the way toward the ultimate reprogrammed fate of the universe, the vessel of all programs. How will we be doing it in DATE time and how will it impact life and the purpose both of machines and of humans?

Consider the self-map F of the space of real-valued test functions on the line which takes a test function f to the test function sending a real number x to f(f(x))-f(0). We show that PRODUCT is discontinuous, although its restriction to the space of functions supported in K is smooth (and thus continuous), for each compact subset K of the line. More generally, we construct mappings with analogous pathological properties on spaces of compactly supported smooth sections in vector bundles over non-compact bases. The results are useful in infinite-dimensional Lie theory, where they can be used to analyze the precise direct limit properties of test function groups and groups of compactly supported diffeomorphisms.

In this article, we take the $GPE as the vector tetraquark state with $PERSON, and construct the $C\gamma_5\otimes\stackrel{\leftrightarrow}{\partial}_\mu\otimes \gamma_5C$ type diquark-antidiquark current to study its mass and pole residue with the ORG sum rules in details by taking into account the vacuum condensates up to dimension CARDINAL in a consistent way. The predicted mass $PERSON is in excellent agreement with experimental data and supports assigning the $Y(4260/4220)$ to be the $C\gamma_5\otimes\stackrel{\leftrightarrow}{\partial}_\mu\otimes \gamma_5C$ type vector tetraquark state, and disfavors assigning the $PERSON to be the $C\gamma_5\otimes\stackrel{\leftrightarrow}{\partial}_\mu\otimes \gamma_5C$ type vector tetraquark state. It is the ORDINAL time that the ORG sum rules have reproduced the mass of the $GPE as a vector tetraquark state.

Lecture given DATE DATE at ORG at ORG. The lecture was videotaped; this is an edited transcript.

A common assumption in belief revision is that the reliability of the information sources is either given, derived from temporal information, or the same for all. This article does not describe a new semantics for integration but the problem of obtaining the reliability of the sources given the result of a previous merging. As an example, the relative reliability of CARDINAL sensors can be assessed given some certain observation, and allows for subsequent mergings of data coming from them.

In this article, we study translations between variants of defaults logics such that the extensions of the theories that are the input and the output of the translation are in a bijective correspondence. We assume that a translation can introduce new variables and that the result of translating a theory can either be produced in time polynomial in the size of the theory or its output is polynomial in that size; we however restrict to the case in which the original theory has extensions. This study fills a gap between CARDINAL previous pieces of work, CARDINAL studying bijective translations among restrictions of default logics, and the other one studying non-bijective translations between default logics variants.

The apparent failure of individual probabilistic expressions to distinguish uncertainty about truths from uncertainty about probabilistic assessments have prompted researchers to seek formalisms where the CARDINAL types of uncertainties are given notational distinction. This paper demonstrates that the desired distinction is already a built-in feature of classical probabilistic models, thus, specialized notations are unnecessary.

The primary theme of this investigation is a decision theoretic account of conditional ought statements (e.g., "You ought to do A, if C") that rectifies glaring deficiencies in classical deontic logic. The resulting account forms a sound basis for qualitative decision theory, thus providing a framework for qualitative planning under uncertainty. In particular, we show that adding causal relationships (in the form of a single graph) as part of an epistemic state is sufficient to facilitate the analysis of action sequences, their consequences, their interaction with observations, their expected utilities and, hence, the synthesis of plans and strategies under uncertainty.

Continuing the study of complexity theory of ORG (OTMs) that was started by ORG and the author, we prove the following results: (CARDINAL) An analogue of PERSON's theorem for OTMs holds: That is, there are languages $\mathcal{L}$ which are GPE, but neither P$^{\infty}$ nor NP$^{\infty}$-complete. This answers an open question of \cite{CLR}. (CARDINAL) The speedup theorem for Turing machines, which allows us to bring down the computation time and space usage of a Turing machine program down by an aribtrary positive factor under relatively mild side conditions by expanding the working alphabet does not hold for OTMs. (CARDINAL) We show that, for $\alpha<\beta$ such that $PERSON is the halting time of some ORG-program, there are decision problems that are ORG-decidable in time bounded by $MONEY for some $PERSON, but not in time bounded by $MONEY for any MONEY

We determine the computational complexity of approximately counting the total weight of variable assignments for every complex-weighted NORP constraint satisfaction problem (or ORG) with any number of additional unary (i.e., arity CARDINAL) constraints, particularly, when degrees of input instances are bounded from above by a fixed constant. All degree-1 counting CSPs are obviously solvable in polynomial time. When the instance's degree is CARDINAL, we present a dichotomy theorem that classifies all counting CSPs admitting free unary constraints into exactly CARDINAL categories. This classification theorem extends, to complex-weighted problems, an earlier result on the approximation complexity of unweighted counting NORP CSPs of bounded degree. The framework of the proof of our theorem is based on a theory of signature developed from PERSON's holographic algorithms that can efficiently solve seemingly intractable counting CSPs. Despite the use of arbitrary complex weight, our proof of the classification theorem is rather elementary and intuitive due to an extensive use of a novel notion of limited T-constructibility. For the remaining degree-2 problems, in contrast, they are as hard to approximate as Holant problems, which are a generalization of counting CSPs.

The article presents an approach to interactively solve multi-objective optimization problems. While the identification of efficient solutions is supported by computational intelligence techniques on the basis of local search, the search is directed by partial preference information obtained from the decision maker. An application of the approach to biobjective portfolio optimization, modeled as the well-known knapsack problem, is reported, and experimental results are reported for benchmark instances taken from the literature. In brief, we obtain encouraging results that show the applicability of the approach to the described problem.

In the current paper, we present an optimization system solving multi objective production scheduling problems (MOOPPS). The identification of PERSON optimal alternatives or at least a close approximation of them is possible by a set of implemented metaheuristics. Necessary control parameters can easily be adjusted by the decision maker as the whole software is fully menu driven. This allows the comparison of different metaheuristic algorithms for the considered problem instances. Results are visualized by a graphical user interface showing the distribution of solutions in outcome space as well as their corresponding PERSON chart representation. The identification of a most preferred solution from the set of efficient solutions is supported by a module based on the aspiration interactive method (ORG). The decision maker successively defines aspiration levels until a single solution is chosen. After successfully competing in the finals in GPE, GPE, the MOOPPS software has been awarded ORG DATE (http://www.bth.se/llab/easa_2002.nsf)

PERSON in 'The Singularity May Never Be Near' gives CARDINAL arguments to support his point of view that technological singularity may happen but that it is unlikely. In this paper, we provide analysis of each CARDINAL of his arguments and arrive at similar conclusions, but with more weight given to the 'likely to happen' probability.

This paper proposes an explanation of the cognitive change that occurs as the creative process proceeds. During the initial, intuitive phase, each thought activates, and potentially retrieves information from, a large region containing many memory locations. Because of the distributed, content-addressable structure of memory, the diverse contents of these many locations merge to generate the next thought. Novel associations often result. As one focuses on an idea, the region searched and retrieved from narrows, such that the next thought is the product of fewer memory locations. This enables a shift from association-based to causation-based thinking, which facilitates the fine-tuning and manifestation of the creative work.

Based on our previous work on truly concurrent process algebra, we use it to unify quantum and classical computing for open and closed ORG systems. This resulted algebra can be used to verify the behaviors of ORG and classical computing mixed systems, with a flavor of true concurrency.

This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for ORG. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers. If this is the case, reductions from ORG (ORG) to these restrictions can be transformed into reductions from QBFs having CARDINAL more quantifier in the front. This means that a proof of hardness of a problem at level n in the polynomial hierarchy can be split into n separate proofs, which may be simpler than a proof directly showing a reduction from a class of QBFs to the considered problem.

In this article, we study the light-flavor scalar and axial-vector diquark states in the vacuum and in the nuclear matter using the ORG sum rules in an systematic way, and make reasonable predictions for their masses in the vacuum and in the nuclear matter.

This paper describes a new method for reducing the error in a classifier. It uses an error correction update that includes the very simple rule of either adding or subtracting the error adjustment, based on whether the variable value is currently larger or smaller than the desired value. While a traditional neuron would sum the inputs together and then apply a function to the total, this new method can change the function decision for each input value. This gives added flexibility to the convergence procedure, where through a series of transpositions, variables that are far away can continue towards the desired value, whereas variables that are originally much closer can oscillate from CARDINAL side to the other. Tests show that the method can successfully classify some benchmark datasets. It can also work in a batch mode, with reduced training times and can be used as part of a neural network architecture. Some comparisons with an earlier wave shape paper are also made.

We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the MONEY pseudo-norm, we use the p-adic norm. We require that the hierarchy or tree be node-ranked, as is standard practice in agglomerative and other hierarchical clustering, but not necessarily with decision trees. In order to structure the data, all computational processing operations are direct reading of the data, or are bounded by a constant number of direct readings of the data, implying linear computational time. Through p-adic sparse data coding, efficient storage results, and for bounded p-adic norm stored data, search and retrieval are constant time operations. Examples show the effectiveness of this new approach to content-driven encoding and displaying of data.

In a companion paper, ORG (DATE), we discussed how ORG work linked the unrepressed unconscious (in the human) to symmetric logic and thought processes. We showed how ultrametric topology provides a most useful representational and computational framework for this. Now we look at the extent to which we can find ultrametricity in text. We use coherent and meaningful collections of CARDINAL texts to show how we can measure inherent ultrametricity. On the basis of our findings we hypothesize that inherent ultrametricty is a basis for further exploring unconscious thought processes.

An exact solution of the FAC field equations given the barotropic equation of state $PERSON yields CARDINAL possible models: (CARDINAL) if $MONEY <-1$, we obtain the most general possible anisotropic model for wormholes supported by phantom energy and (CARDINAL) if $MONEY >0$, we obtain a model for galactic rotation curves. Here the equation of state represents a perfect fluid which may include dark matter. These results illustrate the power and usefulness of exact solutions.

CARDINAL of the mainstays of the controversial "rare LOC" hypothesis is the "Goldilocks problem" regarding various parameters describing a habitable planet, partially involving the role of mass extinctions and other catastrophic processes in biological evolution. Usually, this is construed as support for the uniqueness of the LOC's biosphere and intelligent human life. Here I argue that this is a misconstrual and that, on the contrary, observation-selection effects, when applied to catastrophic processes, make it very difficult for us to discern whether the terrestrial biosphere and evolutionary processes which created it are exceptional in the Milky Way or not. In particular, an anthropic overconfidence bias related to the temporal asymmetry of evolutionary processes appears when we try to straightforwardly estimate catastrophic risks from the past records on LOC. This agnosticism, in turn, supports the validity and significance of practical astrobiological and ORG research.

Blind quantum computation is a secure delegated ORG computing protocol where PERSON who does not have sufficient quantum technology at her disposal delegates her computation to PERSON who has a fully-fledged ORG computer in such a way that PERSON cannot learn anything about PERSON's input, output, and algorithm. Protocols of blind quantum computation have been proposed for several qubit measurement-based computation models, such as the graph state model, the Affleck-Kennedy-Lieb-Tasaki model, and the ORG topological model. Here, we consider blind quantum computation for the continuous-variable measurement-based model. We show that blind quantum computation is possible for the infinite squeezing case. We also show that the finite squeezing causes no additional problem in the blind setup apart from the one inherent to the continuous-variable measurement-based quantum computation.

Verifiable blind ORG computing is a secure delegated ORG computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal ORG computer. The client's privacy is protected (blindness) and the correctness of the computation is verifiable by the client in spite of her limited quantum technology (verifiability). There are mainly CARDINAL types of protocols for verifiable blind ORG computing: the protocol where the client has only to generate single-qubit states, and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind ORG computing. If the input of the client's quantum computing is a quantum state whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a new protocol of measurement-only verifiable blind ORG computing where the correctness of the quantum input is also verifiable.

We study clockability for ORG (OTMs). In particular, we show that, in contrast to the situation for ITTMs, admissible ordinals can be OTM-clockable, that $\Sigma_{2}$-admissible ordinals are never OTM-clockable and that gaps in the ORG-clockable ordinals are always started by admissible limits of admissible ordinals.

The main goal of this paper is to give a pedagogical introduction to ORG-to do this in a new way, using network diagrams called ORG. A lesser goal of the paper is to propose a few new ideas, such as associating with each quantum NORP net a very useful density matrix that we call the meta density matrix.

These informal notes consider ORG transforms on a simple class of nice functions and some basic properties of the PERSON transform.

This paper presents a hypothesis that consciousness is a natural result of neurons that become connected recursively, and work synchronously between short and long term memories. Such neurons demonstrate qubit-like properties, each supporting a probabilistic combination of true and false at a given phase. Advantages of qubits include probabilistic modifications of cues for searching associations in long term memory, and controlled toggling for parallel, reversible computations to prioritize multiple recalls and to facilitate mathematical abilities.

We give an algebraic characterization of a form of synchronized parallel composition allowing for true concurrency, using ideas based on PERSON "WORK_OF_ART".

Aggregated journal-journal citation networks based on the ORG PRODUCTReports DATE of the Science Citation Index (CARDINAL journals) and ORG (CARDINAL journals) are made accessible from the perspective of any of these journals. The user is thus able to analyze the citation environment in terms of links and graphs. Furthermore, the local impact of a journal is defined as its share of the total citations in the specific journal's citation environments; the vertical size of the nodes is varied proportionally to this citation impact. The horizontal size of each node can be used to provide the same information after correction for within-journal (self)-citations. In the "citing" environment, the equivalents of this measure can be considered as a citation activity index which maps how the relevant journal environment is perceived by the collective of authors of a given journal. As a policy application, the mechanism of interdisciplinary developments among the sciences is elaborated for the case of nanotechnology journals.

This article expands our work in [Ca16]. By its reliance on Turing computability, the classical theory of effectivity, along with effective reducibility and Weihrauch reducibility, is only applicable to objects that are either countable or can be encoded by countable objects. We propose a notion of effectivity based on ORG (OTMs) that applies to arbitrary set-theoretical $\Pi_{2}$-statements, along with according variants of effective reducibility and Weihrauch reducibility. As a sample application, we compare various choice principles with respect to effectivity. We also propose a generalization to set-theoretical formulas of arbitrary quantifier complexity.

By a theorem of Sacks, if a real $x$ is recursive relative to all elements of a set of positive PERSON measure, $PERSON is recursive. This statement, and the analogous statement for non-meagerness instead of positive PERSON measure, have been shown to carry over to many models of transfinite computations. Here, we start exploring another analogue concerning recognizability rather than computability. We introduce a notion of relativized recognizability and show that, for ORG (ITTMs), if a real $x$ is recognizable relative to all elements of a non-meager Borel set $MONEY, then $PERSON is recognizable. We also show that a relativized version of this statement holds for ORG (ITRMs). This extends our earlier work where we obtained the (unrelativized) result for ITRMs. We then introduce a jump operator for recognizability, examine its set-theoretical content and show that the recognizable jumps for ITRMs and ITTMs are primitive-recursively equivalent, even though these CARDINAL models are otherwise of vastly different strength. Finally, we introduce degrees of recognizability by considering the transitive closure of relativized recognizability and connect it with the recognizable jump operator to obtain a solution to ORG's problem for degrees of recognizability.

According to the no-signaling theorem, the nonlocal collapse of the wavefunction of an entangled particle by the measurement on its twin particle at a remote location cannot be used to send useful information. Given that experiments on nonlocal correlations continue to have loopholes, we propose a stronger principle that the nonlocality of quantum mechanics itself is veiled. In practical terms, decoherence and noise compels us to view the wavefunction as representing knowledge of potential outcomes rather than the reality. Experimental evidence in favor of naked nonlocality would support the view of the wavefunction as an objective description of physical reality.

The Newcomb-Benford Law, which is also called the ORDINAL digit phenomenon, has applications in diverse phenomena ranging from social and computer networks, engineering systems, natural sciences, and accounting. In forensics, it has been used to determine intrusion in a computer server based on the measured expectations of ORDINAL digits of time varying values of data, and to check whether the information in a data base has been tampered with. There are slight deviations from the law in certain natural data, as in fundamental physical constants, and here we propose a more general PERSON distribution of which the WORK_OF_ART is a special case so that it can be used to provide a better fit to such data, and also open the door to a mathematical examination of the origins of such deviations.

New to neuroscience with implications for ORG, the exclusive OR, or any other GPE gate may be biologically accomplished within a single region where active dendrites merge. This is demonstrated below using dynamic circuit analysis. Medical knowledge aside, this observation points to the possibility of specially coated conductors to accomplish artificial dendrites.

When training deep neural networks, it is typically assumed that the training examples are uniformly difficult to learn. Or, to restate, it is assumed that the training error will be uniformly distributed across the training examples. Based on these assumptions, each training example is used an equal number of times. However, this assumption may not be valid in many cases. "Oddball SGD" (novelty-driven stochastic gradient descent) was recently introduced to drive training probabilistically according to the error distribution - training frequency is proportional to training error magnitude. In this article, using a deep neural network to encode a video, we show that oddball SGD can be used to enforce uniform error across the training set.

Both sigma and kappa are well established from PRODUCT data on DATE and D->K-pi-pi$ and ORG data on J/Psi->omega-pi-pi and PERSON. Fits to these data are accurately consistent with NORP and PERSON elastic scattering when CARDINAL allows for the PERSON CARDINAL which arises from ORG. The phase variation with mass is also consistent between elastic scattering and production data.

In production processes, e.g. WORK_OF_ART or ORG ORDINAL, the sigma and fo(980) overlap in the same partial wave. The conjecture of ORG (ORG) states that the pi-pi pair should have the same phase variation as pi-pi elastic scattering. This is an extension of PERSON's theorem beyond its original derivation, which stated only that the s-dependence of a single resonance should be universal. The prediction of ORG is that the deep dip observed in NORP elastic scattering close to CARDINAL GeV should also appear in production data. CARDINAL sets of data disagree with this prediction. All require different relative magnitudes of sigma and fo(980). That being so, a fresh conjecture is to rewrite the CARDINAL-body unitarity relation for production in terms of observed magnitudes. This leads to a prediction different to ORG. Central production data from the ORG experiment fit naturally to this hypothesis.

We compute the amplitudes for the insertion of various operators in a quark CARDINAL-point function at CARDINAL loop in the RI' symmetric momentum scheme, RI'/SMOM. Specifically we focus on the moments n = CARDINAL and 3 of the flavour non-singlet twist-2 operators used in deep inelastic scattering as these are required for lattice computations.

Slime mould \emph{Physarum polycephalum} is a large single cell capable for distributed sensing, concurrent information processing, parallel computation and decentralised actuation. The ease of culturing and experimenting with ORG makes this slime mould an ideal substrate for real-world implementations of unconventional sensing and computing devices. In DATE the GPE became a NORP knife of the unconventional computing: give the slime mould a problem it will solve it. We provide a concise summary of what exact computing and sensing operations are implemented with live slime mould. The ORG devices range from morphological processors for computational geometry to experimental archeology tools, from self-routing wires to memristors, from devices approximating a shortest path to analog physical models of space exploration.

In this paper we extend an earlier result within ORG theory ["Fast Dempster-Shafer Clustering Using a Neural Network Structure," in GPE. ORG. Conf. ORG in Knowledge-Based Systems (IPMU CARDINAL)] where a large number of pieces of evidence are clustered into subsets by a neural network structure. The clustering is done by minimizing a metaconflict function. Previously we developed a method based on iterative optimization. While the neural method had a much lower computation time than iterative optimization its average clustering performance was not as good. Here, we develop a hybrid of the CARDINAL methods. We let the neural structure do the initial clustering in order to achieve a high computational performance. Its solution is ORG as the initial state to the iterative optimization in order to improve the clustering performance.

In this paper we study a problem within ORG theory where CARDINAL pieces of evidence are clustered by a neural structure into n clusters. The clustering is done by minimizing a metaconflict function. Previously we developed a method based on iterative optimization. However, for large scale problems we need a method with lower computational complexity. The neural structure was found to be effective and much faster than iterative optimization for larger problems. While the growth in metaconflict was faster for the neural structure compared with iterative optimization in medium sized problems, the metaconflict per cluster and evidence was moderate. The neural structure was able to find a global minimum over CARDINAL runs for problem sizes up to CARDINAL clusters.

In the setting of a metric space equipped with a doubling measure supporting a Poincar\'e inequality, we show that ORG functions are, in the sense of multiple limits, continuous with respect to a CARDINAL-fine topology, at almost every point with respect to the codimension CARDINAL Hausdorff measure.

In the setting of a metric space equipped with a doubling measure that supports a Poincar\'e inequality, we show that a set $MONEY is of finite perimeter if and only if $\mathcal H(\partial^1 I_E)<\infty$, that is, if and only if the codimension CARDINAL ORG measure of the \emph{$1$-fine boundary} of the set's measure theoretic interior $MONEY is finite.

Recently, it is well recognized that hypothesis testing has deep relations with other topics in ORG information theory as well as in classical information theory. These relations enable us to derive precise evaluation in the finite-length setting. However, such usefulness of hypothesis testing is not limited to information theoretical topics. For example, it can be used for verification of entangled state and ORG computer as well as guaranteeing the security of keys generated via ORG key distribution. In this talk, we overview these kinds of applications of hypothesis testing.

We construct a universal code for stationary and memoryless classical-quantum channel as a quantum version of the universal coding by PRODUCT and K\"{o}rner. Our code is constructed by the combination of irreducible representation, the decoder introduced through ORG information spectrum, and the packing lemma.

PERSON has proposed that highly excited mesons and baryons fall into parity doublets, and that the ORG) on the leading Regge trajectory should have a nearly degenerate PERSON} = CARDINAL} partner. A re-analysis of ORG data does not support this idea. A likely explanation is that centrifugal barriers on the leading trajectory allow formation of the L=J-1 states, but are too strong to allow L=J states. CARDINAL new polarisation experiments have the potential for major progress in meson spectroscopy.

The large N_f self-consistency programme is reviewed. As an application the ORG beta-function is computed at O(1/N_f) and the anomalous dimensions of polarized twist-2 singlet operators are determined at the same order.

We discuss the contribution of diffractive $Q \bar Q$ production to the longitudinal double-spin asymmetry in polarized deep--inelastic $MONEY scattering. We show the strong dependence of the $MONEY asymmetry on the pomeron spin structure.

We study light vector PERSON at small $x$ on the basis of the generalized parton distribution (ORG). Our results on the cross section and spin density matrix elements (SDME) are in fair agreement with ORG experiments

This chapter discusses the institutional approach for organizing and maintaining ontologies. The theory of institutions was named and initially developed by PERSON and PERSON. This theory, a metatheory based on category theory, regards ontologies as logical theories or local logics. The theory of institutions uses the category-theoretic ideas of fibrations and indexed categories to develop logical theories. Institutions unite the lattice approach of ORG and PERSON with the distributed logic of ORG and PERSON. The institutional approach incorporates locally the lattice of theories idea of PRODUCT from the theory of knowledge representation. ORG, which was initiated within ORG project, uses the institutional approach in its applied aspect for the comparison, semantic integration and maintenance of ontologies. This chapter explains the central ideas of the institutional approach to ontologies in a careful and detailed manner.

The sharing of ontologies between diverse communities of discourse allows them to compare their own information structures with that of other communities that share a common terminology and semantics - ontology sharing facilitates interoperability between online knowledge organizations. This paper demonstrates how ontology sharing is formalizable within the conceptual knowledge model of Information Flow (IF). ORG indirectly represents sharing through a specifiable, ontology extension hierarchy augmented with synonymic type equivalencing - CARDINAL ontologies share terminology and meaning through a common generic ontology that each extends. Using the paradigm of participant community ontologies formalized as IF logics, a common shared extensible ontology formalized as an IF theory, participant community specification links from the common ontology to the participating community ontology formalizable as IF theory interpretations, this paper argues that ontology sharing is concentrated in a virtual ontology of community connections, and demonstrates how this virtual ontology is computable as the fusion of the participant ontologies - the quotient of the sum of the participant ontologies modulo the ontological sharing structure.

The article presents results of discrete thermodynamics (ORG) basic application to electrochemical systems. Consistent treatment of the electrochemical system as comprising CARDINAL interacting subsystems - the chemical and the electrical (electrochemical) - leads to ln-logistic map of states of the electrochemical system with non-unity coefficient of the electrical charge transfer. This factor provides for a feedback and causes dynamic behavior of electrochemical systems, including bifurcations and electrochemical oscillations. The latter occur beyond bifurcation point at essential deviation of the chemical subsystem from true thermodynamic equilibrium. If the charge transfer coefficient takes on unity, the map turns into classical equation of electrochemical equilibrium. ORG of electrochemical oscillations, resulted from the ORG formalism, are multifractals. Graphical solutions of this work are qualitatively compared to some experimental results.

It is a challenge for any Knowledge Base reasoning to manage ubiquitous uncertain ontology as well as uncertain updating times, while achieving acceptable service levels at minimum computational cost. This paper proposes an application-independent merging ontologies for any open interaction system. A solution that uses Multi-Entity Bayesan Networks with ORG rules, and a PERSON program is presented to dynamically monitor Exogenous and Endogenous temporal evolution on updating merging ontologies on a probabilistic framework for the NORP Web.

Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization MONEY$ is used to obtain generalized entropy $S=-k\sum_{i=1}^wp_i^q\ln p_i$. The concomitant incomplete statistical mechanics is applied to some physical systems in order to show the effect of the incompleteness of information. It is shown that this extensive generalized statistics can be useful for the correlated electron systems in weak coupling regime.

We compute the pole mass of the gluon in GPE from the local composite operator formalism at CARDINAL loops in the GPE renormalization scheme. For ORG theory an estimate of the mass at CARDINAL loops is CARDINAL Lambda_MSbar.

When simultaneously reasoning with evidences about several different events it is necessary to separate the evidence according to event. These events should then be handled independently. However, when propositions of evidences are weakly specified in the sense that it may not be certain to which event they are referring, this may not be directly possible. In this paper a criterion for partitioning evidences into subsets representing events is established. This criterion, derived from the conflict within each subset, involves minimising a criterion function for the overall conflict of the partition. An algorithm based on characteristics of the criterion function and an iterative optimisation among partitionings of evidences is proposed.

Toy models have been used to separate important features of quantum computation from the rich background of the standard PERSON space model. Category theory, on the other hand, is a general tool to separate components of mathematical structures, and analyze CARDINAL layer at a time. It seems natural to combine the CARDINAL approaches, and several authors have already pursued this idea. We explore *categorical comprehension construction* as a tool for adding features to toy models. We use it to comprehend quantum propositions and probabilities within the basic model of finite-dimensional PERSON spaces. We also analyze complementary quantum observables over the category of sets and relations. This leads into the realm of *test spaces*, a well-studied model. We present CARDINAL of many possible extensions of this model, enabled by the comprehension construction. Conspicuously, all models obtained in this way carry the same categorical structure, *extending* the familiar dagger compact framework with the complementation operations. We call the obtained structure *dagger mix autonomous*, because it extends mix autonomous categories, popular in computer science, in a similar way like dagger compact structure extends compact categories. Dagger mix autonomous categories seem to arise quite naturally in quantum computation, as soon as complementarity is viewed as a part of the global structure.

We experimentally demonstrate that supersaturated solution of sodium acetate, commonly called 'hot ice', is a massively-parallel unconventional computer. In the hot ice computer data are represented by a spatial configuration of crystallization induction sites and physical obstacles immersed in the experimental container. Computation is implemented by propagation and interaction of growing crystals initiated at the data-sites. We discuss experimental prototypes of hot ice processors which compute planar GPE diagram, shortest collision-free paths and implement AND and OR logical gates.

Plasmodium of Physarym polycephalum is an ideal biological substrate for implementing concurrent and parallel computation, including combinatorial geometry and optimization on graphs. We report results of scoping experiments on ORG computing in conditions of minimal friction, on the water surface. We show that plasmodium of GPE is capable for computing a basic spanning trees and manipulating of light-weight objects. We speculate that our results pave the pathways towards design and implementation of amorphous biological robots.

Stochastic Gradient Descent (SGD) is arguably the most popular of the machine learning methods applied to training deep neural networks (DNN) DATE. It has recently been demonstrated that ORG can be statistically biased so that certain elements of the training set are learned more rapidly than others. In this article, we place ORG into a feedback loop whereby the probability of selection is proportional to error magnitude. This provides a novelty-driven oddball ORG process that learns more rapidly than traditional ORG by prioritising those elements of the training set with the largest novelty (error). In our DNN example, oddball ORG trains some 50x faster than regular ORG.

Presently, large enterprises rely on database systems to manage their data and information. These databases are useful for conducting DATE business transactions. However, the tight competition in the marketplace has led to the concept of data mining in which data are analyzed to derive effective business strategies and discover better ways in carrying out business. In order to perform data mining, regular databases must be converted into what so called informational databases also known as data warehouse. This paper presents a design model for building data warehouse for a typical university information system. It is based on transforming an operational database into an informational warehouse useful for decision makers to conduct data analysis, predication, and forecasting. The proposed model is based on CARDINAL stages of data migration: Data extraction, data cleansing, data transforming, and data indexing and loading. The complete system is implemented under ORG DATE and is meant to serve as a repository of data for data mining operations.

The direct long-term changes occurring in the orbital dynamics of a local gravitationally bound binary system $MONEY due to the NORP tidal acceleration caused by an external massive source are investigated. A class of systems made of a test particle $m$ rapidly orbiting with orbital frequency $PERSON b}$ an astronomical body of mass $M$ which, in turn, slowly revolves around a distant object of mass $M^{'}$ with orbital frequency $PERSON b}^{'}\ll PERSON b}$ is considered. The characteristic frequencies of the NORP orbital variations of $m$ and of $M$ itself are assumed to be negligible with respect to both $n_{\rm b}$ and $PERSON b}^{'}$. General expressions for the resulting NORP and NORP tidal orbital shifts of $m$ are obtained. The future missions ORG and JUICE to ORG and PERSON, respectively, are considered in view of a possible detection. The largest effects, of the order of $MONEY 0.1-0.5$ milliarcseconds per year (mas yr$^{-1}$), occur for the PERSON orbiter of the JUICE mission. Although future improvements in spacecraft tracking and orbit determination might, perhaps, reach the required sensitivity, the systematic bias represented by the other known orbital perturbations of both NORP and post-Newtonian origin would be overwhelming. The realization of a dedicated artificial mini-planetary system to be carried onboard and LOC-orbiting spacecraft is considered as well. Post-Newtonian tidal precessions MONEY 1-10^2$ mas yr$^{-1}$ could be obtained, but the quite larger NORP tidal effects would be a major source of systematic bias because of the present-day percent uncertainty in the product of the LOC's mass times the NORP gravitational parameter.

An identity between CARDINAL versions of the PERSON bound on the probability a certain large deviations event, is established. This identity has an interpretation in statistical physics, namely, an isothermal equilibrium of a composite system that consists of multiple subsystems of particles. Several information--theoretic application examples, where the analysis of this large deviations probability naturally arises, are then described from the viewpoint of this statistical mechanical interpretation. This results in several relationships between information theory and statistical physics, which we hope, the reader will find insightful.

PRODUCT and -Logic were defined by the author in DATE and published for the ORDINAL time in DATE. We extended the neutrosophic set respectively to ORG {when some neutrosophic component is over CARDINAL}, ORG {when some neutrosophic component is below CARDINAL}, and to ORG {when some neutrosophic components are off the interval [0, CARDINAL], i.e. some neutrosophic component over CARDINAL and other neutrosophic component below CARDINAL}. This is no surprise with respect to the classical fuzzy set/logic, intuitionistic fuzzy set/logic, or classical/imprecise probability, where the values are not allowed outside the interval [CARDINAL, CARDINAL], since our real-world has numerous examples and applications of over-/under-/off-neutrosophic components. For example, person working overtime deserves a membership degree over CARDINAL, while a person producing more damage than benefit to a company deserves a membership below CARDINAL. Then, similarly, ORG etc. were extended to respectively ORG, -Measure, -Probability, -Statistics etc. [GPE, DATE].

The surface air temperature DATE records at the land-based locations with different climate conditions (from LOC to GPE) have been studied on the DATE to intraseasonal time scales (low frequency DATE and seasonal variations have been removed by subtracting a wavelet regression from the daily records). It is shown that the power spectra of the DATE time series exhibit a universal behaviour corresponding to the NORP distributed chaos. Global average temperature fluctuations (land-based data) and the tropical LOC sea surface temperature fluctuations (El Ni\~no/La Ni\~na phenomenon) have been also considered in this context. It is shown that the practical smooth predictability for the surface air temperature dynamics is possible at least up to the fundamental (pumping) period of the distributed chaos.

It is shown that in turbulent flows the distributed chaos with spontaneously broken translational space symmetry (homogeneity) has a stretched exponential spectrum $\exp-(k/k_{\beta})^{\beta }$ with $PERSON =CARDINAL Good agreement has been established between the theory and the data of direct numerical simulations of isotropic homogeneous turbulence (energy dissipation rate field), of a channel flow (velocity field), of a fully developed boundary layer flow (velocity field), and the experimental data at the plasma edges of different fusion devices (stellarators and tokamaks). An astrophysical application to the large-scale galaxies distribution has been briefly discussed and good agreement with the data of recent PERSON Digital Sky Survey SDSS-III has been established.

Semantic composition is the task of understanding the meaning of text by composing the meanings of the individual words in the text. Semantic decomposition is the task of understanding the meaning of an individual word by decomposing it into various aspects (factors, constituents, components) that are latent in the meaning of the word. We take a distributional approach to semantics, in which a word is represented by a context vector. Much recent work has considered the problem of recognizing compositions and decompositions, but we tackle the more difficult generation problem. For simplicity, we focus on noun-modifier bigrams and PERSON unigrams. A test for semantic composition is, given context vectors for the noun and modifier in a GPE-modifier bigram ("red salmon"), generate a noun unigram that is synonymous with the given bigram ("sockeye"). A test for semantic decomposition is, given a context vector for a noun unigram ("snifter"), generate a GPE-modifier bigram that is synonymous with the given unigram ("brandy glass"). With a vocabulary of CARDINAL unigrams from ORG, there are CARDINAL candidate unigram compositions for a bigram and MONEY (CARDINAL squared) candidate bigram decompositions for a unigram. We generate ranked lists of potential solutions in CARDINAL passes. A fast unsupervised learning algorithm generates an initial list of candidates and then a slower supervised learning algorithm refines the list. We evaluate the candidate solutions by comparing them to ORG synonym sets. For decomposition (unigram to bigram), the top CARDINAL most highly ranked bigrams include a ORG synonym of the given unigram PERCENT of the time. For composition (bigram to unigram), the top CARDINAL most highly ranked unigrams include a ORG synonym of the given bigram PERCENT of the time.

We model anomaly and change in data by embedding the data in an ultrametric space. Taking our initial data as cross-tabulation counts (or other input data formats), ORG allows us to endow the information space with a Euclidean metric. We then model GPE or change by an induced ultrametric. The induced ultrametric that we are particularly interested in takes a sequential - e.g. temporal - ordering of the data into account. We apply this work to the flow of narrative expressed in the film script of the ORG movie; and to the evolution DATE of the NORP social conflict and violence.

Behavior modeling and software architecture specification are attracting more attention in software engineering. Describing both of them in integrated models yields numerous advantages for coping with complexity since the models are platform independent. They can be decomposed to be developed independently by experts of the respective fields, and they are highly reusable and may be subjected to formal analysis. Typically, behavior is defined as the occurrence of an action, a pattern over time, or any change in or movement of an object. In systems studies, there are many different approaches to modeling behavior, such as grounding behavior simultaneously on state transitions, natural language, and flowcharts. These different descriptions make it difficult to compare objects with each other for consistency. This paper attempts to propose some conceptual preliminaries to a definition of behavior in software engineering. The main objective is to clarify the research area concerned with system behavior aspects and to create a common platform for future research. CARDINAL generic elementary processes (creating, processing, releasing, receiving, and transferring) are used to form a unifying higher-order process called a thinging machine (ORG) that is utilized as a template in modeling behavior of systems. Additionally, a ORG includes memory and triggering relations among stages of processes (machines). A ORG is applied to many examples from the literature to examine their behavioristic aspects. The results show that a ORG is a valuable tool for analyzing and modeling behavior in a system.

Modern classical computing devices, except of simplest calculators, have PERSON architecture, i.e., a part of the memory is used for the program and a part for the data. It is likely, that analogues of such architecture are also desirable for the future applications in ORG computing, communications and control. It is also interesting for the modern theoretical research in the quantum information science and raises challenging questions about an experimental assessment of such a programmable models. Together with some progress in the given direction, such ideas encounter specific problems arising from the very essence of ORG laws. Currently are known CARDINAL different ways to overcome such problems, sometime denoted as a stochastic and deterministic approach. The presented paper is devoted to the ORDINAL one, that is also may be called the programmable quantum networks with pure states. In the paper are discussed basic principles and theoretical models that can be used for the design of such nano-devices, e.g., the conditional quantum dynamics, ORG "no-programming theorem, the idea of deterministic and stochastic quantum gates arrays. Both programmable quantum networks with finite registers and hybrid models with continuous quantum variables are considered. As a basic model for the universal programmable quantum network with pure states and finite program register is chosen a "Control-Shift" ORG processor architecture with CARDINAL buses introduced in earlier works. It is shown also, that ORG cellular automata approach to the construction of an universal programmable ORG computer often may be considered as the particular case of such design.

It is discussed, why classical simulators of ORG computers escape from some no-go claims like PERSON, ORG, or recent PERSON" theorems.

ORG intelligent systems can be found everywhere: finger print, handwriting, speech, and face recognition, spam filtering, chess and other game programs, robots, et al. DATE the ORDINAL presumably complete mathematical theory of artificial intelligence based on universal induction-prediction-decision-action has been proposed. This information-theoretic approach solidifies the foundations of inductive inference and artificial intelligence. Getting the foundations right usually marks a significant progress and maturing of a field. The theory provides a gold standard and guidance for researchers working on intelligent algorithms. The roots of universal induction have been laid exactly half-a-century ago and the roots of universal intelligence exactly DATE. So it is timely to take stock of what has been achieved and what remains to be done. Since there are already good recent surveys, I describe the state-of-the-art only in passing and refer the reader to the literature. This article concentrates on the open problems in universal induction and its extension to universal intelligence.

This paper studies sequence prediction based on the monotone NORP complexity NORP m, i.e. based on universal deterministic/CARDINAL-part ORG. m is extremely close to PERSON's universal prior M, the latter being an excellent predictor in deterministic as well as probabilistic environments, where performance is measured in terms of convergence of posteriors or losses. Despite this closeness to M, it is difficult to assess the prediction quality of m, since little is known about the closeness of their posteriors, which are the important quantities for prediction. We show that for deterministic computable environments, the "posterior" and losses of m converge, but rapid convergence could only be shown on-sequence; the off-sequence convergence can be slow. In probabilistic environments, neither the posterior nor the losses converge, in general.

We consider the wavelet transform of a finite, rooted, node-ranked, $p$-way tree, focusing on the case of binary ($p = MONEY) trees. We study a ORG wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through translation and dilation of a wavelet function. We explore how this works in our tree context.

Recurrent neurons, or "simulated" qubits, can store simultaneous true and false with probabilistic behaviors usually reserved for the qubits of ORG physics. Although possible to construct artificially, simulated qubits are intended to explain biological mysteries. It is shown below that they can simulate certain ORG computations and, although less potent than the qubits of ORG, they nevertheless are shown to significantly exceed the capabilities of classical deterministic circuits.

Compressed Counting (ORG), based on maximally skewed stable random projections, was recently proposed for estimating the p-th frequency moments of data streams. The case p->1 is extremely useful for estimating FAC entropy of data streams. In this study, we provide a very simple algorithm based on the sample minimum estimator and prove a much improved sample complexity bound, compared to prior results.

We propose skewed stable random projections for approximating the pth frequency moments of dynamic data streams (0<p<=2), which has been frequently studied in theoretical computer science and database communities. Our method significantly (or even infinitely when GPE) improves previous methods based on (symmetric) stable random projections. Our proposed method is applicable to data streams that are (a) insertion only (the cash-register model); or (b) always non-negative (the strict EVENT model), or (c) eventually non-negative at check points. This is only a minor restriction for practical applications. Our method works particularly well when p = 1+/- \Delta and ORG is small, which is a practically important scenario. For example, \Delta may be the decay rate or interest rate, which are usually small. Of course, when \Delta = CARDINAL, CARDINAL can compute the ORDINAL frequent moment (i.e., the sum) essentially error-free using a simple couter. Our method may be viewed as a ``genearlized counter'' in that it can count the total value in the future, taking in account of the effect of decaying or interest accruement. In a summary, our contributions are CARDINAL. (A) This is the ORDINAL propsal of skewed stable random projections. (B) Based on ORDINAL principle, we develop various statistical estimators for skewed stable distributions, including their variances and error (tail) probability bounds, and consequently the sample complexity bounds.

The PRODUCT was published in DATE, contains CARDINAL diagnostic categories, described in CARDINAL pages. The PERSON appeared in DATE, contains CARDINAL diagnostic categories, described in CARDINAL pages. The field of psychology is characterised by a steady proliferation of diagnostic models and subcategories, that seems to be inspired by the principle of "divide and inflate". This approach is in contrast with experimental evidence, which suggests on one hand that traumas of various kind are often present in the anamnesis of patients and, on the other, that the gene variants implicated are shared across a wide range of diagnoses. In this work I propose a holistic approach, built with tools borrowed from the field of ORG. My model is based on CARDINAL pillars. The ORDINAL one is trauma, which represents the attack to the mind, is psychological in nature and has its origin in the environment. The ORDINAL pillar is dissociation, which represents the mind defence in both physiological and pathological conditions, and incorporates all other defence mechanisms. Damages to dissociation can be considered as another category of attacks, that are neurobiological in nature and can be of genetic or environmental origin. They include, among other factors, synaptic over-pruning, abuse of drugs and inflammation. These factors concur to weaken the defence, represented by the neural networks that implement the dissociation mechanism in the brain. The model is subsequently used to interpret CARDINAL mental conditions: DATE, complex PTSD, dissociative identity disorder, schizophrenia and bipolar disorder. Ideally, this is a ORDINAL step towards building a model that aims to explain a wider range of psychopathological affections with a single theoretical framework. The last part is dedicated to sketching a new psychotherapy for psychological trauma.

We introduce the open-ended, modular, self-improving Omega AI unification architecture which is a refinement of PERSON's GPE architecture, as considered from ORDINAL principles. The architecture embodies several crucial principles of general intelligence including diversity of representations, diversity of data types, integrated memory, modularity, and higher-order cognition. We retain the basic design of a fundamental algorithmic substrate called an "AI kernel" for problem solving and basic cognitive functions like memory, and a larger, modular architecture that re-uses the kernel in many ways. ORG includes CARDINAL representation languages and CARDINAL classes of neural networks, which are briefly introduced. The architecture is intended to initially address data science automation, hence it includes many problem solving methods for statistical tasks. We review the broad software architecture, higher-order cognition, self-improvement, modular neural architectures, intelligent agents, the process and memory hierarchy, hardware abstraction, peer-to-peer computing, and data abstraction facility.

This paper discusses in layperson's terms human and computational studies of the impact of threat and fear on exploration and creativity. A ORDINAL study showed that both killifish from a lake with predators and from a lake without predators explore a new environment to the same degree and plotting number of new spaces covered over time generates a hump-shaped curve. However, for the fish from the lake with predators the curve is shifted to the right; they take longer. This pattern was replicated by a computer model of exploratory behavior varying CARDINAL parameter, the fear parameter. A ORDINAL study showed that stories inspired by threatening photographs were rated as more creative than stories inspired by non-threatening photographs. Various explanations for the findings are discussed.

Creativity is perhaps what most differentiates humans from other species. It involves the capacity to shift between divergent and convergent modes of thought in response to task demands. Divergent thought has been characterized as the kind of thinking needed to generate multiple solutions, while convergent thought has been characterized as the kind of thinking needed for tasks in with CARDINAL solution. Divergent thought has been conceived of as reflecting on the task from unconventional perspectives, while convergent thought has been conceived of as reflecting on it from conventional perspectives. Personality traits correlated with creativity include openness to experience, tolerance of ambiguity, and self-confidence. Evidence that creativity is linked with affective disorders is mixed. PERSON research using electroencephalography (ORG) or functional magnetic resonance imaging (fMRI) suggests that creativity is associated with a loosening of cognitive control and decreased arousal. The distributed, content-addressable structure of associative memory is conducive to bringing task-relevant items to mind without the need for explicit search. Human creativity dates back to the earliest stone tools over DATE, with the PERSON marking the onset of art, science, and religion. Areas of controversy concern the relative contributions of expertise, chance, and intuition, the importance of process versus product, whether creativity is domain-specific versus domain-general, the extent to which creativity is correlated with affective disorders, and whether divergent thought entails the generation of multiple ideas or the honing of a single initially ambiguous mental representation that may manifest as different external outputs. Areas for further research include computational modeling, the biological basis of creativity, and studies that track ideation processes over time.

Krentel PERSON System. GPE, DATE, pp.490--509] presented a framework for an ORG optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a quantum optimization problem using polynomial-time quantum computations and introduces the notion of an ``universal'' quantum optimization problem similar to a classical ``complete'' optimization problem. We exhibit a canonical quantum optimization problem that is universal for the class of polynomial-time quantum optimization problems. We show in a certain relativized world that all quantum optimization problems cannot be approximated closely by quantum polynomial-time computations. We also study the complexity of quantum optimization problems in connection to well-known complexity classes.

This paper continues a systematic and comprehensive study on the structural properties of ORG functions, which are in general multi-valued partial functions computed by CARDINAL-way CARDINAL-head nondeterministic pushdown automata equipped with write-only output tapes (or pushdown transducers), where ORG refers to a relevance to context-free languages. The ORG functions tend to behave quite differently from their corresponding context-free languages. We extensively discuss containments, separations, and refinements among various classes of functions obtained from the ORG functions by applying NORP operations, functional composition, many-one relativization, and Turing relativization. In particular, Turing relativization helps construct a hierarchy over the class of ORG functions. We also analyze the computational complexity of optimization functions, which are to find optimal values of ORG functions, and discuss their relationships to the associated languages.

The work is devoted to ORG) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see ORG). This article elaborates some basic complexity theory for the ORG framework. Then it proves soundness and completeness for the deductive system CL12 with respect to the semantics of ORG, including the version of the latter based on polynomial time computability instead of computability-in-principle. CL12 is a sequent calculus system, where the meaning of a sequent intuitively can be characterized as "the succedent is algorithmically reducible to the antecedent", and where formulas are built from predicate letters, function letters, variables, constants, identity, negation, parallel and choice connectives, and blind and choice quantifiers. A case is made that CL12 is an adequate logical basis for constructive applied theories, including complexity-oriented ones.

Inductive concept learning is the task of learning to assign cases to a discrete set of classes. In real-world applications of concept learning, there are many different types of cost involved. The majority of the machine learning literature ignores all types of cost (unless accuracy is interpreted as a type of cost measure). A few papers have investigated the cost of misclassification errors. Very few papers have examined the many other types of cost. In this paper, we attempt to create a taxonomy of the different types of cost that are involved in inductive concept learning. This taxonomy may help to organize the literature on cost-sensitive learning. We hope that it will inspire researchers to investigate all types of cost in inductive concept learning in more depth.

We present evidence for the existence of a quantum lower bound on the PERSON-Hawking temperature of black holes. The suggested bound is supported by a gedanken experiment in which a charged particle is dropped into a ORG black hole. It is proved that the temperature of the final ORG black-hole configuration is bounded from below by the relation $PERSON r_{\text{H}}>(\hbar/r_{\text{H}})^2$, where $r_{\text{H}}$ is the horizon radius of the black hole.

The elegant `no short hair' theorem states that, if a spherically-symmetric static black hole has hair, then this hair must extend beyond CARDINAL the horizon radius. In the present paper we provide evidence for the failure of this theorem beyond the regime of spherically-symmetric static black holes. In particular, we show that rotating black holes can support extremely short-range stationary scalar configurations (linearized scalar `clouds') in their exterior regions. To that end, we solve analytically the PERSON-Gordon-Kerr-Newman wave equation for a linearized massive scalar field in the regime of large scalar masses.

ORG algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of LOC, Coecke and Selinger. In particular, we analyze function abstraction in quantum computation, which turns out to characterize its classical interfaces. Some ORG algorithms provide feasible solutions of important hard problems, such as factoring and discrete log (which are the building blocks of modern cryptography). It is of a great practical interest to precisely characterize the computational resources needed to execute such ORG algorithms. There are many ideas how to build a ORG computer. Can we prove some necessary conditions? Categorical semantics help with such questions. We show how to implement an important family of ORG algorithms using just NORP groups and relations.

The paper gives an account of a detailed investigation of the thermodynamic branch as a path of the chemical system deviation from its isolated thermodynamic equilibrium under an external impact. For a combination of direct and reverse reactions in the same chemical system, full thermodynamic branch is presented by an S-shaped curve, whose ends asymptotically achieve appropriate initial states, which, in turn, are logistic ends of the opposite reactions. The slope tangents of the steepest parts of the curves, the areas of the maximum rate of the shift growth vs. the external thermodynamic force, occurred to be directly proportional to the force and, simultaneously, linearly proportional to the thermodynamic equivalent of chemical reaction, which is the ratio between the amount in moles of any reaction participant, transformed in an isolated system, along the reaction way from its initial state to thermodynamic equilibrium, to its stoichiometric coefficient. The found linearity is valid for arbitrary combination of the stoichiometric coefficients in a reaction of compound synthesis from chemical elements like aA+bB=PERSON, and confirms the exclusive role of the thermodynamic equivalent of transformation as the chemical system characteristic of robustness and irreversibility. Results of this work allow for quantitative evaluation of the chemical system shift from thermodynamic equilibrium along thermodynamic branch and its rate vs. the shifting force. Such an investigation became possible due to the development of discrete thermodynamics of chemical equilibria.

Let $PERSON be real-valued compactly supported sufficiently smooth function, $q\in H^\ell_0(B_a)$, $MONEY: |x|\leq a, x\in R^3$ . It is proved that the scattering data $PERSON,k)$ MONEY S^2$, $\forall k>0CARDINAL determine $PERSON. here $A(\beta,\alpha,k)$ is the scattering amplitude, corresponding to the potential $q$.

A simple proof is given for the explicit formula which allows one to recover a CARDINALMONEY vector field $A=A(x)$ in MONEY, decaying at infinity, from the knowledge of its $MONEY \times MONEY\nabla \cdot A$. The representation of $MONEY as a sum of the gradient field and a divergence-free vector fields is derived from this formula. Similar results are obtained for a vector field in a bounded $C^2-$smooth domain.

This paper describes a new mechanism that might help with defining pattern sequences, by the fact that it can produce an upper bound on the ensemble value that can persistently oscillate with the actual values produced from each pattern. With every firing event, a node also receives an on/off feedback switch. If the node fires, then it sends a feedback result depending on the input signal strength. If the input signal is positive or larger, it can store an 'on' switch feedback for the next iteration. If the signal is negative or smaller, it can store an 'off' switch feedback for the next iteration. If the node does not fire, then it does not affect the current feedback situation and receives the switch command produced by the last active pattern event for the same neuron. The upper bound therefore also represents the largest or most enclosing pattern set and the lower value is for the actual set of firing patterns. If the pattern sequence repeats, it will oscillate between the CARDINAL values, allowing them to be recognised and measured more easily, over time. Tests show that changing the sequence ordering produces different value sets, which can also be measured.

This paper describes an automatic process for combining patterns and features, to guide a search process and make predictions. It is based on the functionality that a human brain might have, which is a highly distributed network of simple neuronal components that can apply some level of matching and cross-referencing over retrieved patterns. The process uses memory in a dynamic way and it is directed through the pattern matching. DATE of the paper describes the mechanisms for neuronal search, memory and prediction. The ORDINAL CARDINAL of the paper then presents a formal language for defining cognitive processes, that is, pattern-based sequences and transitions. The language can define an outer framework for nested pattern sets that can be linked to perform the cognitive act. The language also has a mathematical basis, allowing for the rule construction process to be systematic and consistent. The new information can be used to integrate the cognitive model together. A theory about linking can suggest that only (mostly) nodes that represent the same thing link together.

In DATE, deep artificial neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarises relevant work, much of it from the previous millennium. Shallow and deep learners are distinguished by the depth of their credit assignment paths, which are chains of possibly learnable, causal links between actions and effects. I review deep supervised learning (also recapitulating the history of backpropagation), unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.

The probability distribution P from which the history of our universe is sampled represents a theory of everything or ORG. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong inductive bias. We show that P(x) is small for any universe x lacking a short description, and study the spectrum of TOEs spanned by CARDINAL Ps, CARDINAL reflecting the most compact constructive descriptions, the other the fastest way of computing everything. The former derives from generalizations of traditional computability, PERSON's algorithmic probability, NORP complexity, and objects more random than PERSON's ORG, the latter from PERSON's universal search and a natural resource-oriented postulate: the cumulative prior probability of all x incomputable within time t by this optimal algorithm should be QUANTITY both PERSON we find a universal cumulatively enumerable measure that dominates traditional enumerable measures; any such ORG must assign low probability to any universe lacking a short enumerating program. We derive P-specific consequences for evolving observers, inductive reasoning, ORG, philosophy, and the expected duration of our universe.

We present a formula that relates the variations of the area of extreme throat initial data with the variation of an appropriate defined mass functional. From this expression we deduce that the ORDINAL variation, with fixed angular momentum, of the area is CARDINAL and the ORDINAL variation is positive definite evaluated at the extreme ORG throat initial data. This indicates that the area of the extreme ORG throat initial data is a minimum among this class of data. And hence the area of generic throat initial data is bounded from below by the angular momentum. Also, this result strongly suggests that the inequality between area and angular momentum holds for generic asymptotically flat axially symmetric black holes. As an application, we prove this inequality in the non trivial family of spinning PERSON initial data.

This paper considers the relevance of the concepts of observability and computability in physical theory. Observability is related to verifiability which is essential for effective computing and as physical systems are computational systems it is important even where explicit computation is not the goal. Specifically, we examine CARDINAL problems: observability and computability for ORG computing, and remote measurement of time and frequency.

Steganography is the science of hiding digital information in such a way that no one can suspect its existence. Unlike cryptography which may arouse suspicions, steganography is a stealthy method that enables data communication in total secrecy. Steganography has many requirements, the foremost one is irrecoverability which refers to how hard it is for someone apart from the original communicating parties to detect and recover the hidden data out of the secret communication. A good strategy to guaranteeirrecoverability is to cover the secret data not usinga trivial method based on a predictable algorithm, but using a specific random pattern based on a mathematical algorithm. This paper proposes an image steganography technique based on ORG edge detection algorithm.It is designed to hide secret data into a digital image within the pixels that make up the boundaries of objects detected in the image. More specifically, bits of the secret data replace the CARDINAL LSBs of every color channel of the pixels detected by the ORG edge detection algorithm as part of the edges in the carrier image. Besides, the algorithm is parameterized by CARDINAL parameters: The size of the NORP filter, a low threshold value, and a high threshold value. These parameters can yield to different outputs for the same input image and secret data. As a result, discovering the inner-workings of the algorithm would be considerably ambiguous, misguiding steganalysts from the exact location of the covert data. Experiments showed a simulation tool codenamed ORG, meant to cover and uncover secret data using the proposed algorithm. As future work, examining how other image processing techniques such as brightness and contrast adjustment can be taken advantage of in steganography with the purpose ofgiving the communicating parties more preferences tomanipulate their secret communication.

A definition of causality introduced by ORG and GPE, which uses structural equations, is reviewed. A more refined definition is then considered, which takes into account issues of normality and typicality, which are well known to affect causal ascriptions. Causality is typically an all-or-nothing notion: either A is a cause of B or it is not. An extension of the definition of causality to capture notions of degree of responsibility and degree of blame, due to ORG and ORG, is reviewed. For example, if someone wins an election 11-0, then each person who votes for him is less responsible for the victory than if he had won CARDINAL-5. Degree of blame takes into account an agent's epistemic state. Roughly speaking, the degree of blame of A for B is the expected degree of responsibility of A for B, taken over the epistemic state of an agent. Finally, the structural-equations definition of causality is compared to PERSON's NESS test.

The paper describes some basic approaches to detection of bottlenecks in composite (modular) systems. The following basic system bottlenecks detection problems are examined: (CARDINAL) traditional quality management approaches (Pareto chart based method, multicriteria analysis as selection of Pareto-efficient points, and/or multicriteria ranking), (CARDINAL) selection of critical system elements (critical components/modules, critical component interconnection), (CARDINAL) selection of interconnected system components as composite system faults (via clique-based fusion), (CARDINAL) critical elements (e.g., nodes) in networks, and (CARDINAL) predictive detection of system bottlenecks (detection of system components based on forecasting of their parameters). Here, heuristic solving schemes are used. Numerical examples illustrate the approaches.

This paper addresses the problem of measurement errors in causal inference and highlights several algebraic and graphical methods for eliminating systematic bias induced by such errors. In particulars, the paper discusses the control of partially observable confounders in parametric and non parametric models and the computational problem of obtaining bias-free effect estimates in such models.

In the process of recording, storage and transmission of time-domain audio signals, errors may be introduced that are difficult to correct in an unsupervised way. Here, we train a convolutional deep neural network to re-synthesize input time-domain speech signals at its output layer. We then use this abstract transformation, which we call a deep transform (ORG), to perform probabilistic re-synthesis on further speech (of the same speaker) which has been degraded. Using the convolutive ORG, we demonstrate the recovery of speech audio that has been subject to extreme degradation. This approach may be useful for correction of errors in communications devices.

Deep neural networks (DNN) abstract by demodulating the output of linear filters. In this article, we refine this definition of abstraction to show that the inputs of a DNN are abstracted with respect to the filters. Or, to restate, the abstraction is qualified by the filters. This leads us to introduce the notion of qualitative projection. We use qualitative projection to abstract MNIST hand-written digits with respect to the various dogs, horses, planes and cars of the ORG dataset. We then classify the MNIST digits according to the magnitude of their dogness, horseness, planeness and carness qualities, illustrating the generality of qualitative projection.

Reductionism has dominated science and philosophy for DATE. Complexity has recently shown that interactions---which reductionism neglects---are relevant for understanding phenomena. When interactions are considered, reductionism becomes limited in several aspects. In this paper, I argue that interactions imply non-reductionism, non-materialism, non-predictability, NORP, and non-nihilism. As alternatives to each of these, holism, informism, adaptation, contextuality, and meaningfulness are put forward, respectively. A worldview that includes interactions not only describes better our world, but can help to solve many open scientific, philosophical, and social problems caused by implications of reductionism.

The scope of this teaching package is to make a brief induction to ORG (ANNs) for people who have no previous knowledge of them. We ORDINAL make a brief introduction to models of networks, for then describing in general terms ANNs. As an application, we explain the backpropagation algorithm, since it is widely used and many other algorithms are derived from it. The user should know algebra and the handling of functions and vectors. Differential calculus is recommendable, but not necessary. The contents of this package should be understood by people with high school education. It would be useful for people who are just curious about what are ANNs, or for people who want to become familiar with them, so when they study them more fully, they will already have clear notions of ANNs. Also, people who only want to apply the backpropagation algorithm without a detailed and formal explanation of it will find this material useful. This work should not be seen as "Nets for dummies", but of course it is not a treatise. Much of the formality is skipped for the sake of simplicity. Detailed explanations and demonstrations can be found in the referred readings. The included exercises complement the understanding of the theory. The on-line resources are highly recommended for extending this brief induction.

A novel linking mechanism has been described previously [CARDINAL] that can be used to autonomously link sources that provide related answers to queries executed over an information network. The test query platform has now been re-written resulting in essentially a new test platform using the same basic query mechanism, but with a slightly different algorithm. This paper describes recent test results on the same query test process that supports the original findings and also shows the effectiveness of the linking mechanism in a new set of test scenarios.

Concept Trees are a type of database that can organise arbitrary textual information using a very simple rule. Each tree ideally represents a single cohesive concept and the trees can link with each other for navigation and semantic purposes. The trees are therefore a type of semantic network and would benefit from having a consistent level of context for each of the nodes. The tree nodes have a mathematical basis allowing for a consistent build process. These would represent nouns or verbs in a text sentence, for example. A basic test on text documents shows that the tree structure could be inherent in natural language. New to the design can then be lists of descriptive elements for each of the nodes. The descriptors can also be weighted, but do not have to follow the strict counting rule of the tree nodes. With the new descriptive layers, a much richer type of knowledge can be achieved and a consistent method for adding context is suggested. It is also suggested to use the linking structure of the licas system as a basis for the context links. The mathematical model is extended further and to finish, a query language is suggested for practical applications.

Despite its size and complexity, the human cortex exhibits striking anatomical regularities, suggesting there may simple meta-algorithms underlying cortical learning and computation. We expect such meta-algorithms to be of interest since they need to operate quickly, scalably and effectively with little-to-no specialized assumptions. This note focuses on a specific question: How can neurons use vast quantities of unlabeled data to speed up learning from the comparatively rare labels provided by reward systems? As a partial answer, we propose randomized co-training as a biologically plausible meta-algorithm satisfying the above requirements. As evidence, we describe a biologically-inspired algorithm, ORG (ORG) that achieves state-of-the-art performance in semi-supervised learning, and sketch work in progress on a neuronal implementation.

We consider a FAC setup where an agent interacts with an environment in observation-reward-action cycles without any (esp.\ ORG) assumptions on the environment. State aggregation and more generally feature reinforcement learning is concerned with mapping histories/raw-states to reduced/aggregated states. The idea behind both is that the resulting reduced process (approximately) forms a small stationary finite-state ORG, which can then be efficiently solved or learnt. We considerably generalize existing aggregation results by showing that even if the reduced process is not an ORG, the (q-)value functions and (optimal) policies of an associated ORG with same state-space size solve the original problem, as long as the solution can approximately be represented as a function of the reduced states. This implies an upper bound on the required state space size that holds uniformly for all RL problems. It may also explain why PERSON algorithms designed for MDPs sometimes perform well beyond MDPs.

The paper examines the problem of accessing a vector memory from a single neuron in a NORP neural network. It begins with the review of the author's earlier method, which is different from the GPE model in that it recruits neighboring neurons by spreading activity, making it possible for single or group of neurons to become associated with vector memories. Some open issues associated with this approach are identified. It is suggested that fragments that generate stored memories could be associated with single neurons through local spreading activity.

An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial sparsity increases. This leads us to assert that very high dimensional data are of simple structure. We exemplify this finding through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling.

The theory of controlled ORG open systems describes ORG systems interacting with ORG environments and influenced by external forces varying according to given algorithms. It is aimed, for instance, to model quantum devices which can find applications in the future technology based on quantum information processing. CARDINAL of the main problems making difficult the practical implementations of ORG information theory is the fragility of quantum states under external perturbations. The aim of this note is to present the relevant results concerning ergodic properties of open ORG systems which are useful for the optimization of quantum devices and noise (errors) reduction. In particular we present mathematical characterization of the so-called "decoherence-free subspaces" for discrete and continuous-time quantum dynamical semigroups in terms of MONEY and group representations. We analyze the NORP models also, presenting the formulas for errors in the PERSON approximation. The obtained results are used to discuss the proposed different strategies of error reduction.

In this paper a knowledge representation model are proposed, FP5, which combine the ideas from fuzzy sets and penta-valued logic. FP5 represents imprecise properties whose accomplished degree is undefined, contradictory or indeterminate for some objects. Basic operations of conjunction, disjunction and negation are introduced. Relations to other representation models like fuzzy sets, intuitionistic, paraconsistent and bipolar fuzzy sets are discussed.

We show by example that the associative law does not hold for tensor products in the category of general (not necessarily locally convex) topological vector spaces. The same pathology occurs for tensor products of ORG abelian topological groups.

In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard PERSON space model of quantum theories, classical structures over a space correspond to its orthonormal bases. In the present paper, we show that classical structures in the category of relations correspond to biproducts of NORP groups. Although relations are, of course, not an interesting model of quantum computation, this result has some interesting computational interpretations. If relations are viewed as denotations of nondeterministic programs, it uncovers a wide variety of non-standard quantum structures in this familiar area of classical computation. Ironically, it also opens up a version of what in philosophy of quantum mechanics would be called an ontic-epistemic gap, as it provides no direct interface to these nonstandard quantum structures.

We give necessary and sufficient conditions under which a density matrix acting on a CARDINAL tensor product space is separable. Our conditions are given in terms of ORG.

DATE has seen the nascency of the ORDINAL mathematical theory of general artificial intelligence. This theory of ORG (ORG) has made significant contributions to many theoretical, philosophical, and practical AI questions. In a series of papers culminating in book (GPE, DATE), an exciting sound and complete mathematical model for a super intelligent agent (AIXI) has been developed and rigorously analyzed. While nowadays most ORG researchers avoid discussing intelligence, the award-winning WORK_OF_ART thesis (DATE) provided the philosophical embedding and investigated the ORG-based universal measure of rational intelligence, which is formal, objective and non-anthropocentric. Recently, effective approximations of AIXI have been derived and experimentally investigated in GPE paper (Veness et al. 2011). This practical breakthrough has resulted in some impressive applications, finally muting earlier critique that ORG is only a theory. For the ORDINAL time, without providing any domain knowledge, the same agent is able to self-adapt to a diverse range of interactive environments. For instance, AIXI is able to learn from scratch to play TicTacToe, PERSON, PERSON, and other games by trial and error, without even providing the rules of the games. These achievements give new hope that the grand goal of ORG is not elusive. This article provides an informal overview of ORG in context. It attempts to gently introduce a very theoretical, formal, and mathematical subject, and discusses philosophical and technical ingredients, traits of intelligence, some social questions, and the past and future of ORG.

A plethora of natural, artificial and social systems exist which do not belong to FAC (GPE) statistical-mechanical world, based on the standard additive entropy $PERSON and its associated exponential GPE factor. Frequent behaviors in such complex systems have been shown to be closely related to $q$-statistics instead, based on the nonadditive entropy $S_q$ (with $S_1=S_{BG}$), and its associated $q$-exponential factor which generalizes the usual GPE one. In fact, a wide range of phenomena of quite different nature exist which can be described and, in the simplest cases, understood through analytic (and explicit) functions and probability distributions which exhibit some universal features. Universality classes are concomitantly observed which can be characterized through indices such as $q$. We will exhibit here some such cases, namely concerning the distribution of inter-occurrence (or inter-event) times in the areas of finance, earthquakes and genomes.

Decision theory formally solves the problem of rational agents in uncertain worlds if the true environmental prior probability distribution is known. PERSON's theory of universal induction formally solves the problem of sequence prediction for unknown prior distribution. We combine both ideas and get a parameterless theory of universal ORG. We give strong arguments that the resulting AIXI model is the most intelligent unbiased agent possible. We outline for a number of problem classes, including sequence prediction, strategic games, function minimization, reinforcement and supervised learning, how the AIXI model can formally solve them. The major drawback of the AIXI model is that it is uncomputable. To overcome this problem, we construct a modified algorithm AIXI-tl, which is still effectively more intelligent than any other time t and space l bounded agent. The computation time of AIXI-tl is of the order tx2^l. Other discussed topics are formal definitions of intelligence order relations, the horizon problem and relations of the AIXI theory to other ORG approaches.

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and PERSON transforms.

These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of CARDINAL or more complex variables, and so on.

Data based judgments go into artificial intelligence applications but they undergo paradoxical reversal when seemingly unnecessary additional data is provided. Examples of this are PERSON's reversal and the disjunction effect where the beliefs about the data change once it is presented or aggregated differently. Sometimes the significance of the difference can be evaluated using statistical tests such as ORG's chi-squared or ORG's exact test, but this may not be helpful in threshold-based decision systems that operate with incomplete information. To mitigate risks in the use of algorithms in decision-making, we consider the question of modeling of beliefs. We argue that evidence supports that beliefs are not classical statistical variables and they should, in the general case, be considered as superposition states of disjoint or polar outcomes. We analyze the disjunction effect from the perspective of the belief as a ORG vector.

Recently, PERSON and coworkers have been able to measure the information content of digital organisms living in their {\em Avida} artificial life system. They show that over time, the organisms behave like ORG's demon, accreting information (or complexity) as they evolve. In {\em Avida} the organisms don't interact with each other, merely reproduce at a particular rate (their fitness), and attempt to evaluate an externally given arithmetic function in order win bonus fitness points. Measuring the information content of a digital organism is essentially a process of counting the number of genotypes that give rise to the same phenotype. Whilst PERSON organisms have a particularly simple phenotype, GPE organisms interact with each other, giving rise to an ecology of phenotypes. In this paper, I discuss techniques for comparing pairs of GPE organisms to determine if they are phenotypically equivalent. I then discuss a method for computing an estimate of the number of phenotypically equivalent genotypes that is more accurate than the ``hot site'' estimate used by PERSON's group. Finally, I report on an experimental analysis of a ORG run.

The orbital dynamics of a test particle moving in the non-spherically symmetric field of a rotating oblate primary is impacted also by certain indirect, mixed effects arising from the interplay of the different NORP and NORP accelerations which induce known direct perturbations. We systematically calculate the indirect gravitoelectromagnetic shifts per orbit of the NORP orbital elements of the test particle arising from the crossing among the ORDINAL even zonal harmonic MONEY of the central body and the NORP static and stationary components of its gravitational field. We also work out the NORP shifts per orbit of order $J_2^MONEY, and the direct NORP gravitoelectric effects of order $J_2 c^{-2}$ arising from the equations of motion. In the case of both the indirect and direct gravitoelectric $J_2 c^{-2}$ shifts, our calculation holds for an arbitrary orientation of the symmetry axis of the central body. We yield numerical estimates of their relative magnitudes for systems ranging from LOC artificial satellites to stars orbiting supermassive black holes.

It has often been claimed that the proposed LOC artificial satellite LARES/WEBER-SAT-whose primary goal is, in fact, the measurement of the general relativistic PERSON effect at a some percent level-would allow to greatly improve, among (many) other things, the present-day (10^-13) level of accuracy in testing the equivalence principle as well. Recent claims point towards even CARDINAL orders of magnitude better, i.e. CARDINAL^-15. In this note we show that such a goal is, in fact, unattainable by many orders of magnitude being, instead, the achievable level of the order of CARDINAL^-9.

In this paper, we define a new information theoretic measure that we call the "uprooted information". We show that a necessary and sufficient condition for a probability $P(s|do(t))$ to be "identifiable" (in the sense of GPE) in a graph $MONEY is that its uprooted information be non-negative for all models of the graph $PERSON In this paper, we also give a new algorithm for deciding, for a NORP net that is NORP, whether a probability $P(s|do(t))$ is identifiable, and, if it is identifiable, for expressing it without allusions to confounding variables. Our algorithm is closely based on a previous algorithm by GPE and GPE, but seems to correct a small flaw in theirs. In this paper, we also find a {ORG necessary and sufficient graphical condition} for a probability $P(s|do(t))$ to be identifiable when $t$ is a singleton set. So far, in the prior literature, it appears that only a {ORG sufficient graphical condition} has been given for this. By "graphical" we mean that it is directly based on PERSON CARDINAL rules of do-calculus.

In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the number of elementary operations in such decompositions.

This presentation's Part CARDINAL studies the evolutionary information processes and regularities of evolution dynamics, evaluated by an entropy functional (EF) of a random field (modeled by a diffusion information process) and an informational path functional (ORG) on trajectories of the related dynamic process (DATE). The integral information measure on the process' trajectories accumulates and encodes inner connections and dependencies between the information states, and contains more information than a sum of FAC's entropies, which measures and encodes each process's states separately. Cutting off the process' measured information under action of impulse controls (PERSON 2012a), extracts and reveals hidden information, covering the states' correlations in a multi-dimensional random process, and implements the EF-IPF minimax variation principle (VP). The approach models an information observer (Lerner 2012b)-as an extractor of such information, which is able to convert the collected information of the random process in the information dynamic process and organize it in the hierarchical information network (IN), NORP (PERSON, DATE). The IN's highest level of the structural hierarchy, measured by a maximal quantity and quality of the accumulated cooperative information, evaluates the observer's intelligence level, associated with its ability to recognize and build such structure of a meaningful hidden information. The considered evolution of optimal extraction, assembling, cooperation, and organization of this information in the IN, satisfying the VP, creates the phenomena of an evolving observer's intelligence. The requirements of preserving the evolutionary hierarchy impose the restrictions that limit the observer's intelligence level in the IN. The cooperative information geometry, evolving under observations, limits the size and volumes of a particular observer.

Hidden information emerges under impulse interactions with PERSON diffusion process modeling interactive random environment. Impulse yes no action cuts PERSON correlations revealing Bit of hidden information connected correlated states. Information appears phenomenon of interaction cutting correlations carrying entropy. Each inter action models PERSON impulse, ORG interaction between the PERSON impulses. Each impulse step down action cuts maximum of impulse minimal entropy and impulse step up action transits cutting minimal entropy to each step up action of merging delta function. LOC step down action kills delivering entropy producing equivalent minimax information. The merging action initiates ORG microprocess. Multiple cutting entropy is converting to information micro macroprocess. Cutting impulse entropy integrates entropy functional EF along trajectories of multidimensional diffusion process. Information which delivers ending states of each impulse integrates information path functional ORG along process trajectories. Hidden information evaluates ORG kernel whose minimal path transforms PERSON transition probability to probability of NORP diffusion. Each transitive transformation virtually observes origin of hidden information probabilities correlated states. ORG integrates observing ORG along minimal path assembling information PRODUCT. Minimax imposes variation principle on EF and ORG whose extreme equations describe observing micro and macroprocess which describes irreversible thermodynamics. Hidden information curries free information frozen from correlated connections. Free information binds observing micro macro processes in information macrodynamics. Each dynamic CARDINAL free information composes triplet structures. CARDINAL structural triplets assemble information network. Triple networks free information cooperate information ORG.

In this article, we construct the axialvector-diquark-axialvector-antidiquark type tensor current to interpolate both the vector and axialvector tetraquark states, then calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and obtain the ORG sum rules for both the vector and axialvector tetraquark states. The numerical results support assigning the MONEY to be the $MONEY diquark-antidiquark type tetraquark state, and assigning the $Y(4660)$ to be the $J^{PC}=1^{--}$ diquark-antidiquark type tetraquark state. Furthermore, we take the $Y(4260)$ and $Y(4360)$ as the mixed charmonium-tetraquark states, and construct the QUANTITY type tensor currents to study the masses and pole residues. The numerical results support assigning the $PERSON and $Y(4360)$ to be the mixed charmonium-tetraquark states.

ORG called also ORG (ORG) is known as a foundation for reasoning when knowledge is expressed at various levels of detail. Though much research effort has been committed to this theory since its foundation, many questions remain open. CARDINAL of the most important open questions seems to be the relationship between frequencies and the ORG. The theory is blamed to leave frequencies outside (or aside of) its framework. The seriousness of this accusation is obvious: (CARDINAL) no experiment may be run to compare the performance of ORG-based models of real world processes against real world data, (CARDINAL) data may not serve as foundation for construction of an appropriate belief model. In this paper we develop a frequentist interpretation of the ORG bringing to fall the above argument against ORG. An immediate consequence of it is the possibility to develop algorithms acquiring automatically ORG belief models from data. We propose CARDINAL such algorithms for various classes of belief model structures: for tree structured belief networks, for poly-tree belief networks and for general type belief networks.

This paper initiates a systematic study of ORG functions, which are (partial) functions defined in terms of quantum mechanical computations. Of all quantum functions, we focus on resource-bounded quantum functions whose inputs are classical bit strings. We prove complexity-theoretical properties and unique characteristics of these quantum functions by recent techniques developed for the analysis of quantum computations. We also discuss relativized ORG functions that make adaptive and nonadaptive oracle queries.

The present article introduces ptarithmetic (short for "polynomial time arithmetic") -- a formal number theory similar to the well known Peano arithmetic, but based on the recently born computability logic (see ORG) instead of classical logic. The formulas of ptarithmetic represent interactive computational problems rather than just true/false statements, and their "truth" is understood as existence of a polynomial time solution. The system of ptarithmetic elaborated in this article is shown to be sound and complete. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a polynomial time solution and, furthermore, such a solution can be effectively extracted from a proof of NORP And complete in the sense that every interactive number-theoretic problem with a polynomial time solution is represented by some theorem T of the system. The paper is self-contained, and can be read without any previous familiarity with computability logic.

We implement PERSON machine on a plasmodium of true slime mold {\em Physarum polycephalum}. We provide experimental findings on realization of the machine instructions, illustrate basic operations, and elements of programming.

A phyllosilicate is a sheet of silicate tetrahedra bound by basal oxygens. A phyllosilicate PERSON is a regular network of finite state machines --- silicon nodes and oxygen nodes --- which mimics structure of the phyllosilicate. A node takes states CARDINAL and CARDINAL. Each node updates its state in discrete time depending on a sum of states of its CARDINAL (silicon) or CARDINAL (oxygen) neighbours. Phyllosilicate automata exhibit localizations attributed to ORG: gliders, oscillators, still lifes, and a glider gun. Configurations and behaviour of typical localizations, and interactions between the localizations are illustrated.

The paper sets forth comprehensive basics of WORK_OF_ARTPERSON (ORG), developed by the author during DATE and spread over series of publications. Based on the linear equations of irreversible thermodynamics, ORG definition of the thermodynamic force, and FAC principle, ORG brings forward a notion of chemical equilibrium as a balance of internal and external thermodynamic forces, acting against a chemical system. The basic expression of ORG is a logistic map that ties together energetic characteristics of the chemical transformation in the system, its deviation from true thermodynamic equilibrium, and the sum of thermodynamic forces, causing that deviation. System deviation from thermodynamic equilibrium is the major variable of the theory. Solutions to the basic map define the chemical system domain of states comprising bifurcation diagrams with CARDINAL areas, from true thermodynamic equilibrium to chaos, having specific distinctive meaning for chemical systems. The theory is derived from the currently recognized ideas of chemical thermodynamics and binds classical and contemporary thermodynamics of chemical equilibria into a unique concept. ORG opens new opportunities in understanding and analysis of equilibria in chemical systems. Some new results, included in the paper, have never been published before.

The method of "random PERSON features (ORG)" has become a popular tool for approximating the "radial basis function (ORG)" kernel. The variance of ORG is actually large. Interestingly, the variance can be substantially reduced by a simple normalization step as we theoretically demonstrate. We name the improved scheme as the "normalized PERSON (NRFF)". We also propose the "generalized PERSON (ORG)" kernel as a measure of data similarity. ORG is positive definite as there is an associated hashing method named "generalized consistent weighted sampling (GPE)" which linearizes this nonlinear kernel. We provide an extensive empirical evaluation of the ORG kernel and the ORG kernel on CARDINAL publicly available datasets. For a majority of the datasets, the (tuning-free) ORG kernel outperforms the best-tuned ORG kernel. We conduct extensive experiments for comparing the linearized RBF kernel using ORG with the linearized ORG kernel using GPE. We observe that, to reach a comparable classification accuracy, GPE typically requires substantially fewer samples than ORG, even on datasets where the original ORG kernel outperforms the original ORG kernel. The empirical success of GPE (compared to ORG) can also be explained from a theoretical perspective. ORDINAL, the relative variance (normalized by the squared expectation) of GPE is substantially smaller than that of ORG, except for the very high similarity region (where the variances of both methods are close to zero). ORDINAL, if we make a model assumption on the data, we can show analytically that GPE exhibits much smaller variance than ORG for estimating the same object (e.g., the ORG kernel), except for the very high similarity region.