Complete set of quasi-conserved quantities for spinning particles around Kerr

We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss the implications for the motion of spinning particles on Kerr spacetime where the quasi-constants of motion are shown not to be in complete involution.

Ranking Sets of Objects: The Complexity of Avoiding Impossibility Results

The problem of lifting a preference order on a set of objects to a preference order on a family of subsets of this set is a fundamental problem with a wide variety of applications in AI. The process is often guided by axioms postulating properties the lifted order should have. Well-known impossibility results by Kannai and Peleg and by Barbera and Pattanaik tell us that some desirable axioms – namely dominance and (strict) independence – are not jointly satisfiable for any linear order on the objects if all non-empty sets of objects are to be ordered. On the other hand, if not all non-empty sets of objects are to be ordered, the axioms are jointly satisfiable for all linear orders on the objects for some families of sets. Such families are very important for applications as they allow for the use of lifted orders, for example, in combinatorial voting. In this paper, we determine the computational complexity of recognizing such families. We show that it is \Pi_2^p-complete to decide for a given family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for all linear orders on the objects if the lifted order needs to be total. Furthermore, we show that the problem remains coNP-complete if the lifted order can be incomplete. Additionally, we show that the complexity of these problems can increase exponentially if the family of sets is not given explicitly but via a succinct domain restriction. Finally, we show that it is NP-complete to decide for a family of subsets whether dominance and independence or dominance and strict independence are jointly satisfiable for at least one linear order on the objects.

Using Fishburne’s sequences in suitable modeling used for sample data

This article deals with probabilistic and statistical modeling of managerial decision-making in the economy based on sample data for the previous periods of time. For better definition, the study is limited to Markowitz’s models in the problem of finding an effective portfolio of the field in the third information situation. The third information situation is a widespread decision-making situation and is characterized by the fact that the decision-maker sets, according to his opinion, are a linear order relation on the components of an unknown probabilistic distribution of the states of the economic environment. Often, from the point of view of the decision-maker, the components of an unknown probability distribution of the states of the economic environment must satisfy a partially reinforced linear order relation. As a result, the use of traditional statistical estimates turns out to be impossible, while the following question arises, which is practically not studied in the scientific literature. In this case, what formulas should be used to find statistical estimates and, above all, estimates of unknown probabilities of the state of the economic environment? As an estimate of an unknown probability distribution, we proposed to use the Fishburne sequence that satisfies all available constraints, while corresponding to the opinion of the decision maker and the linear order relation given by him. Fishburne sequences are a generalization of the well-known Fishburne formulas. It is fundamentally important that any Fishburne sequence satisfies a simple linear order relation, and under certain conditions, a partially strengthened linear order relation. Particular attention is paid to the entropic properties of generalized Fishburne progressions, which represent the most important class of Fishburne sequences, as well as the use of generalized Fishburne progressions to take into account the opinion of the decision maker. Such a scheme for estimating an unknown probability distribution has been developed, which makes it possible to achieve the correctness of probabilistic and statistical modeling, as well as appropriate consideration of the opinion of the decision-maker, uncertainty and risk.

Anachronisms in Charles Dickens’s ‘Great Expectations’: A Case Study Based on Gerard Genette’s Structural Narratology: الإيقاع الزمني في رواية تشارلز ديكنز "آمال عظيمة" دراسة حالة في ضوء تقنيات السرد البنائي عند جيرارد جينيت

This paper deals with the narrative order of time in Charles Dickens’s novel Great Expectations. Time is crucial in narratological structure as it establishes a logical relation for events in the narrative. Besides, a narrative develops its point of view through the voices in the narrative. This point of view is called focalization. This paper assumes that the sequence of events in Dickens’s Great Expectations does not follow a linear order and consequently, the point of focalization changes throughout the narrative. Accordingly, the current paper intends to investigate the order of narration in the novel. It intends to explore the ultimate thematic concern of the novel as well. The discussion will be in the light of Gerard Genette’s narratological structure and will be applied on Dickens’s Great Expectations. It is the 13th novel in his independent literary works. It has been published unillustrated in 36 weekly instalments in All the Year Round from 1860 through 1861. Then, it has been published in three volumes by Chapman & Hall in1861. The narrative voice has a great impact on the story’s timeline and on the readers because it is narrated in the first-person voice by the protagonist, Philip Pirrip. (Davis, 2007: P 126) The analysis is based on Genette’s theorization of time order in telling a story and communicating a broader point of view that the author intends to make throughout the whole narrative structure.

Biased statistical learning of closed-class items

In natural languages, closed-class items predict open-class items but not the other way around. For example, in English, if there is a determiner there will be a noun, but nouns can occur with or without determiners. Here we asked whether statistical learning of closed-class items is also asymmetrical. In three experiments we exposed adults to a miniature language with the one-way dependency “if X then Y”: if X was present, Y was also present, but Y could occur without X. We created different versions of the language in order to ask whether learning depended on which category (X or Y) was an open or closed class. In one condition, X had the main properties of a closed class and Y had the main properties of an open class; in a contrasting condition, X had properties of an open class and Y had properties of a closed class. Learners’ exposure in these two conditions was otherwise identical. Learning was significantly better with closed-class X. Additional experiments demonstrated that it is the perceptual distinctiveness of closed-class items that drives learners to analyze them differently, and that the mathematical relationship between closed- and open-class items influences learning more strongly than their linear order. These results suggest that statistical learning is biased: learners privilege computations in which closed-class items are predictive of, rather than predicted by, open-class items. We suggest that the distributional asymmetries of closed-class items in natural languages—and perhaps the asymmetrical structure of linguistic representations—may arise in part from this learning bias.

Canonical Set Theory for Classic Mathematics: A Linear Order on Finite Groups and Structures, with A Natural Extension To Infinite Structures

We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order on all finite groups, that is well behaved with respect to cardinality. In fact, if $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G$. Internally, there is also a canonical order for the elements of any finite group $G$, and we find equivalent objects. This allows us to find the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and a minimal set of independent equations that define the group is obtained. Examples are given, using all groups with less than ten elements, to illustrate the procedure for finding all groups of $n$ elements, and we order them externally and internally. The canonical block form of the symmetry group $\Delta_4$ is given and we find its automorphisms. These results are extended to the infinite case. A real number is an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, also. We make brief mention on the calculus of real numbers. In general, we are able to represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects of all types are well assigned to tree structures. We conclude with comments on type theory and future work on computational and physical aspects of these representations.

Testing the weak cosmic censorship conjecture for a Reissner–Nordström–de Sitter black hole surrounded by perfect fluid dark matter

In this paper, we test the weak cosmic censorship conjecture (WCCC) for the Reissner–Nordström–de Sitter (RN-dS) black hole surrounded by perfect fluid dark matter. We consider a spherically symmetric perturbation on deriving linear and non-linear order perturbation inequalities by applying a new version of gedanken experiments well accepted from the work of Sorce and Wald. Contrary to the well-known result that the Reissner–Nordström (RN) black hole could be overcharged under linear order particle accretion it is hereby shown that the same black hole in perfect fluid dark matter with cosmological parameter cannot be overcharged. Considering a realistic scenario in which black holes cannot be considered to be in vacuum we investigate the contribution of dark matter and cosmological constant in the overcharging process of an electrically charged black hole. We demonstrate that the black hole can be overcharged only when two fields induced by dark matter and cosmological parameter are completely balanced. Further we present a remarkable result that a black hole cannot be overcharged beyond a certain threshold limit for which the effect arising from the cosmological constant dominates over the effect by the perfect fluid dark matter. Thus even for a linear accretion process, the black hole cannot always be overcharged and hence obeys the WCCC in general. This result would continue to be fulfilled for non-linear order accretion.

N3LO gravitational quadratic-in-spin interactions at G4

We compute the N3LO gravitational quadratic-in-spin interactions at G4 in the post-Newtonian (PN) expansion via the effective field theory (EFT) of gravitating spinning objects for the first time. This result contributes at the 5PN order for maximally-spinning compact objects, adding the spinning case to the static sector at this PN accuracy. This sector requires extending the EFT of a spinning particle beyond linear order in the curvature to include higher-order operators quadratic in the curvature that are relevant at this PN order. We make use of a diagrammatic expansion in the worldline picture, and rely on our recent upgrade of the EFTofPNG code, which we further extend to handle this sector. Similar to the spin-orbit sector, we find that the contributing three-loop graphs give rise to divergences, logarithms, and transcendental numbers. However, in this sector all of these features conspire to cancel out from the final result, which contains only finite rational terms.