scholarly journals Probability Models of Distributed Proof Generation for zk-SNARK-Based Blockchains

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3016
Author(s):  
Yuri Bespalov ◽  
Alberto Garoffolo ◽  
Lyudmila Kovalchuk ◽  
Hanna Nelasa ◽  
Roman Oliynykov
Keyword(s):  
Markov Chains ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Time Slot ◽  
Generation Process ◽  
Probability Models ◽  
Consensus Protocol ◽  
Current Block ◽  
The One ◽  
First Time

The paper is devoted to the investigation of the distributed proof generation process, which makes use of recursive zk-SNARKs. Such distributed proof generation, where recursive zk-SNARK-proofs are organized in perfect Mercle trees, was for the first time proposed in Latus consensus protocol for zk-SNARKs-based sidechains. We consider two models of a such proof generation process: the simplified one, where all proofs are independent (like one level of tree), and its natural generation, where proofs are organized in partially ordered set (poset), according to tree structure. Using discrete Markov chains for modeling of corresponding proof generation process, we obtained the recurrent formulas for the expectation and variance of the number of steps needed to generate a certain number of independent proofs by a given number of provers. We asymptotically represent the expectation as a function of the one variable n/m, where n is the number of provers m is the number of proofs (leaves of tree). Using results obtained, we give numerical recommendation about the number of transactions, which should be included in the current block, idepending on the network parameters, such as time slot duration, number of provers, time needed for proof generation, etc.

Stochastic domination and Markovian couplings

2000 ◽  
Vol 32 (4) ◽  
pp. 1064-1076 ◽  
Author(s):  
F. Javier López ◽  
Servet Martínez ◽  
Gerardo Sanz
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Sufficient Conditions ◽  
Stochastic Domination ◽  
Jackson Networks ◽  
Partially Ordered ◽  
Continuous Time Markov Chains ◽  
Necessary And Sufficient

For continuous-time Markov chains with semigroups P, P' taking values in a partially ordered set, such that P ≤ stP', we show the existence of an order-preserving Markovian coupling and give a way to construct it. From our proof, we also obtain the conditions of Brandt and Last for stochastic domination in terms of the associated intensity matrices. Our result is applied to get necessary and sufficient conditions for the existence of Markovian couplings between two Jackson networks.

scholarly journals Atlas of ticks (Acari: Argasidae, Ixodidae) in Germany

2021 ◽  
Author(s):  
Franz Rubel ◽  
Katharina Brugger ◽  
Lidia Chitimia-Dobler ◽  
Hans Dautel ◽  
Elisabeth Meyer-Kayser ◽  
...  
Keyword(s):  
Tick Species ◽  
Migratory Birds ◽  
Dermacentor Reticulatus ◽  
Ixodid Ticks ◽  
Federal States ◽  
Ixodes Frontalis ◽  
Argas Reflexus ◽  
The One ◽  
Argasid Tick ◽  
First Time

AbstractAn updated and increased compilation of georeferenced tick locations in Germany is presented here. This data collection extends the dataset published some years ago by another 1448 new tick locations, 900 locations of which were digitized from literature and 548 locations are published here for the first time. This means that a total of 3492 georeferenced tick locations is now available for Germany. The tick fauna of Germany includes two species of Argasidae in the genera Argas and Carios and 19 species of Ixodidae in the genera Dermacentor, Haemaphysalis, and Ixodes, altogether 21 tick species. In addition, three species of Ixodidae in the genera Hyalomma (each spring imported by migratory birds) and Rhipicephalus (occasionally imported by dogs returning from abroad with their owners) are included in the tick atlas. Of these, the georeferenced locations of 23 tick species are depicted in maps. The occurrence of the one remaining tick species, the recently described Ixodes inopinatus, is given at the level of the federal states. The most common and widespread tick species is Ixodes ricinus, with records in all 16 federal states. With the exception of Hamburg, Dermacentor reticulatus was also found in all federal states. The occurrence of the ixodid ticks Ixodes canisuga, Ixodes frontalis, Ixodes hexagonus and I. inopinatus were documented in at least 11 federal states each. The two mentioned argasid tick species were also documented in numerous federal states, the pigeon tick Argas reflexus in 11 and the bat tick Carios vespertilionis in seven federal states. The atlas of ticks in Germany and the underlying digital dataset in the supplement can be used to improve global tick maps or to study the effects of climate change and habitat alteration on the distribution of tick species.

Intuitionistic fuzzy two-factor variance analysis of movie ticket sales

2021 ◽  
pp. 1-11
Author(s):  
Velichka Traneva ◽  
Stoyan Tranev
Keyword(s):  
Comparative Analysis ◽  
Real Data ◽  
Intuitionistic Fuzzy Sets ◽  
Real Numbers ◽  
Data Set ◽  
Important Method ◽  
Ticket Sales ◽  
Intuitionistic Fuzzy ◽  
The One ◽  
First Time

Analysis of variance (ANOVA) is an important method in data analysis, which was developed by Fisher. There are situations when there is impreciseness in data In order to analyze such data, the aim of this paper is to introduce for the first time an intuitionistic fuzzy two-factor ANOVA (2-D IFANOVA) without replication as an extension of the classical ANOVA and the one-way IFANOVA for a case where the data are intuitionistic fuzzy rather than real numbers. The proposed approach employs the apparatus of intuitionistic fuzzy sets (IFSs) and index matrices (IMs). The paper also analyzes a unique set of data on daily ticket sales for a year in a multiplex of Cinema City Bulgaria, part of Cineworld PLC Group, applying the two-factor ANOVA and the proposed 2-D IFANOVA to study the influence of “ season ” and “ ticket price ” factors. A comparative analysis of the results, obtained after the application of ANOVA and 2-D IFANOVA over the real data set, is also presented.

scholarly journals Experiential ownership and body ownership are different phenomena

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Caleb Liang ◽  
Wen-Hsiang Lin ◽  
Tai-Yuan Chang ◽  
Chi-Hong Chen ◽  
Chen-Wei Wu ◽  
...  
Keyword(s):  
Conscious Experience ◽  
Distinct Type ◽  
Body Part ◽  
The Body ◽  
Body Ownership ◽  
Rubber Hand ◽  
Person Perspective ◽  
The One ◽  
First Time ◽  
Full Body

AbstractBody ownership concerns what it is like to feel a body part or a full body as mine, and has become a prominent area of study. We propose that there is a closely related type of bodily self-consciousness largely neglected by researchers—experiential ownership. It refers to the sense that I am the one who is having a conscious experience. Are body ownership and experiential ownership actually the same phenomenon or are they genuinely different? In our experiments, the participant watched a rubber hand or someone else’s body from the first-person perspective and was touched either synchronously or asynchronously. The main findings: (1) The sense of body ownership was hindered in the asynchronous conditions of both the body-part and the full-body experiments. However, a strong sense of experiential ownership was observed in those conditions. (2) We found the opposite when the participants’ responses were measured after tactile stimulations had ceased for 5 s. In the synchronous conditions of another set of body-part and full-body experiments, only experiential ownership was blocked but not body ownership. These results demonstrate for the first time the double dissociation between body ownership and experiential ownership. Experiential ownership is indeed a distinct type of bodily self-consciousness.

Address of the President Lord Blackett, O. M., C. H. at the Anniversary Meeting, 1 December 1969

1970 ◽  
Vol 174 (1037) ◽  
pp. 403-417
Keyword(s):  
Immunological Response ◽  
Immunological Tolerance ◽  
Cell Mediated Immunity ◽  
Specific Cell ◽  
Subsequent Work ◽  
The One ◽  
First Time ◽  
Improved Methods ◽  
Specific Tolerance ◽  
Immunological Barrier

The Copley Medal is awarded to Sir Peter Medawar, C. B. E., F. R. S. Medawar’s first major contribution was to prove conclusively that skin grafts made between different individuals usually fail because of an immunological response made by the recipient against foreign antigens in the donor’s cells, and then to show that the most important mechanism was a specific cell-mediated immunity due to lymphocytes. In attempting to find means of preventing the response against grafted tissues, without impairing immunological capacity in other respects, Medawar made a second major contribution by showing for the first time that it was possible to induce specific tolerance of foreign antigens by administering them to very young animals. His subsequent work, directed towards achieving practical means of overcoming the immunological barrier to tissue transplantation, led him on the one hand to investigate improved methods of inducing specific immunological tolerance and, on the other, to use antiserum against lymphocytes to suppress the damaging effects of these cells. His successful results in experimental animals have indicated the way to their possible application in Man. Medawar’s work has throughout been distinguished by a penetrating clarity of thought combined with insight, and by elegant and original experimental design. He also has a justly high reputation for his analyses and predictions in wider fields of biology, and his study of scientific method.

Information Retrieval Systems, an Algebraic Approach I1

1981 ◽  
Vol 4 (3) ◽  
pp. 551-603
Author(s):  
Zbigniew Raś
Keyword(s):  
Information Retrieval ◽  
Boolean Algebra ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Algebraic Approach ◽  
Partially Ordered ◽  
Retrieval Systems ◽  
Information Retrieval Systems ◽  
Present Part ◽  
L Systems

This paper is the first of the three parts of work on the information retrieval systems proposed by Salton (see [24]). The system is defined by the notions of a partially ordered set of requests (A, ⩽), the set of objects X and a monotonic retrieval function U : A → 2X. Different conditions imposed on the set A and a function U make it possible to obtain various classes of information retrieval systems. We will investigate systems in which (A, ⩽) is a partially ordered set, a lattice, a pseudo-Boolean algebra and Boolean algebra. In my paper these systems are called partially ordered information retrieval systems (po-systems) lattice information retrieval systems (l-systems); pseudo-Boolean information retrieval systems (pB-systems) and Boolean information retrieval systems (B-systems). The first part concerns po-systems and 1-systems. The second part deals with pB-systems and B-systems. In the third part, systems with a partial access are investigated. The present part discusses the method for construction of a set of attributes. Problems connected with the selectivity and minimalization of a set of attributes are investigated. The characterization and the properties of a set of attributes are given.

CsOH and its Lighter Homologues – a Comparison

2014 ◽  
Vol 69 (11-12) ◽  
pp. 1229-1236
Author(s):  
Matthias Wörsching ◽  
Constantin Hoch
Keyword(s):  
Gas Phase ◽  
Room Temperature ◽  
Structure Type ◽  
Alkali Metal Hydroxide ◽  
X Ray ◽  
Raman Spectroscopic ◽  
Cesium Hydroxide ◽  
Free Ion ◽  
The One ◽  
First Time

Abstract Cesium hydroxide, CsOH, was for the first time characterised on the basis of single-crystal data. The structure is isotypic to the one of the room-temperature modification of NaOH and can be derived from the NaCl structure type thus allowing the comparison of all alkali metal hydroxide structures. Raman spectroscopic investigations show the hydroxide anion to behave almost as a free ion as in the gas phase. The X-ray investigations indicate possible H atom positions.

scholarly journals Gamma Astrometric Measurement Experiment: testing General Relativity with a small mission

2007 ◽  
Vol 3 (S248) ◽  
pp. 290-291 ◽  
Author(s):  
A. Vecchiato ◽  
M. G. Lattanzi ◽  
M. Gai ◽  
R. Morbidelli
Keyword(s):  
General Relativity ◽  
Solar Eclipse ◽  
Galactic Center ◽  
The Sun ◽  
Measurement Experiment ◽  
The One ◽  
First Time ◽  
Bending Of Light

AbstractGAME (Gamma Astrometric Measurement Experiment) is a concept for an experiment whose goal is to measure from space the γ parameter of the Parameterized Post-Newtonian formalism, by means of a satellite orbiting at 1 AU from the Sun and looking as close as possible to its limb. This technique resembles the one used during the solar eclipse of 1919, when Dyson, Eddington and collaborators measured for the first time the gravitational bending of light. Simple estimations suggest that, possibly within the budget of a small mission, one could reach the 10−6level of accuracy with ~106observations of relatively bright stars at about 2° apart from the Sun. Further simulations show that this result could be reached with only 20 days of measurements on stars ofV≤ 17 uniformly distributed. A quick look at real star densities suggests that this result could be greatly improved by observing particularly crowded regions near the galactic center.

scholarly journals Each join-completion of a partially ordered set in the solution of a universal problem

1974 ◽  
Vol 17 (4) ◽  
pp. 406-413 ◽  
Author(s):  
Jürgen Schmidt
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Unique Extension ◽  
Partially Ordered ◽  
Special Cases

The main result of this paper is the theorem in the title. Only special cases of it seem to be known so far. As an application, we obtain a result on the unique extension of Galois connexions. As a matter of fact, it is only by the use of Galois connexions that we obtain the main result, in its present generality.

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