scholarly journals Convexity of graph-restricted games induced by minimum partitions

2019 ◽  
Vol 53 (3) ◽  
pp. 841-866 ◽  
Author(s):  
Alexandre Skoda
Keyword(s):  
Necessary Conditions ◽  
Minimum Weight ◽  
Weighted Graph ◽  
Connected Components ◽  
Weighted Graphs ◽  
Classical Definition ◽  
Restricted Game ◽  
Definition Of ◽  
Adjacent Cycles ◽  
Restricted Games

We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition 𝒫min is i nduced by the deletion of the minimum weight edges. We provide five necessary conditions on the graph edge-weights to have inheritance of convexity from the underlying game to the restricted game associated with 𝒫min. Then, we establish that these conditions are also sufficient for a weaker condition, called ℱ-convexity, obtained by restriction of convexity to connected subsets. Moreover, we prove that inheritance of convexity for Myerson restricted game associated with a given graph G is equivalent to inheritance of ℱ-convexity for the 𝒫min-restricted game associated with a particular weighted graph G′ built from G by adding a dominating vertex, and with only two different edge-weights. Then, we prove that G is cycle-complete if and only if a specific condition on adjacent cycles is satisfied on G′.

Complexity of inheritance of ℱ-convexity for restricted games induced by minimum partitions

2020 ◽  
Vol 54 (1) ◽  
pp. 143-161
Author(s):  
A. Skoda
Keyword(s):  
Cooperative Game ◽  
Polynomial Time ◽  
Minimum Weight ◽  
Connected Components ◽  
Communication Graph ◽  
Convex Game ◽  
Restricted Game ◽  
Restricted Games ◽  
Unweighted Graph

Let G = (N, E, w) be a weighted communication graph. For any subset A ⊆ N, we delete all minimum-weight edges in the subgraph induced by A. The connected components of the resultant subgraph constitute the partition 𝒫min(A) of A. Then, for every cooperative game (N, v), the 𝒫min-restricted game (N, v̅) is defined by v̅(A)=∑F∈𝒫min(A)v(F) for all A ⊆ N. We prove that we can decide in polynomial time if there is inheritance of ℱ-convexity, i.e., if for every ℱ-convex game the 𝒫min-restricted game is ℱ-convex, where ℱ-convexity is obtained by restricting convexity to connected subsets. This implies that we can also decide in polynomial time for any unweighted graph if there is inheritance of convexity for Myerson’s graph-restricted game.

scholarly journals Constant Factor Approximation for Tracking Paths and Fault Tolerant Feedback Vertex Set

2021 ◽  
pp. 23-38
Author(s):  
Václav Blažej ◽  
Pratibha Choudhary ◽  
Dušan Knop ◽  
Jan Matyáš Křišt’an ◽  
Ondřej Suchý ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Fault Tolerant ◽  
Minimum Weight ◽  
Weighted Graph ◽  
Constant Factor ◽  
Weighted Graphs ◽  
Feedback Vertex Set ◽  
Fixed Integer ◽  
Vertex Set

AbstractConsider a vertex-weighted graph G with a source s and a target t. Tracking Paths requires finding a minimum weight set of vertices (trackers) such that the sequence of trackers in each path from s to t is unique. In this work, we derive a factor 66-approximation algorithm for Tracking Paths in weighted graphs and a factor 4-approximation algorithm if the input is unweighted. This is the first constant factor approximation for this problem. While doing so, we also study approximation of the closely related r-Fault Tolerant Feedback Vertex Set problem. There, for a fixed integer r and a given vertex-weighted graph G, the task is to find a minimum weight set of vertices intersecting every cycle of G in at least $$r+1$$ r + 1 vertices. We give a factor $$\mathcal {O}(r^2)$$ O ( r 2 ) approximation algorithm for r-Fault Tolerant Feedback Vertex Set if r is a constant.

The Development of Forgiveness

2020 ◽  
pp. 401-418
Author(s):  
Robert D. Enright ◽  
Jacqueline Y. Song
Keyword(s):  
Necessary Conditions ◽  
Practical Application ◽  
Important Work ◽  
Future Directions ◽  
Developmental Progression ◽  
Forgiveness Education ◽  
Cognitive Work ◽  
Adolescents And Adults ◽  
Forgiveness Therapy ◽  
Definition Of

The psychology of forgiveness originated from the creative and important work on the development of justice initiated by Piaget in 1932 and extended by Kohlberg in 1969. The scientific study of forgiveness is quite new, having emerged in print in 1989, with an examination of the developmental progression in children’s, adolescents’, and adults’ thinking about the necessary conditions for them to offer forgiveness to another person. In this chapter, the authors first review the definition of forgiveness, followed by this early cognitive work. They then turn to a discussion of the measurement of forgiveness correlates of forgiveness. The practical application of this construct is seen in the development of forgiveness therapy and forgiveness education, which the authors discuss in light of the empirical findings. Future directions for forgiveness studies are considered.

scholarly journals AB0677 REVISING THE DEFINITION OF REACTIVE ARTHRITIS AND DIFFERENTIATION FROM UNDIFFERENTIATED SPONDYLOARTHRITIS

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1633.2-1634
Author(s):  
F. Cosan ◽  
O. M. Gedar
Keyword(s):  
Causative Agent ◽  
Reactive Arthritis ◽  
Case Reports ◽  
Experimental Studies ◽  
Classification Criteria ◽  
General Definition ◽  
Parasitic Infections ◽  
Undifferentiated Spondyloarthritis ◽  
Classical Definition ◽  
Definition Of

Background:Reactive arthritis (ReA) is defined by 1999 ACR criteria as arthritis preceding a bacterial genitourinary (GUS) or gastrointestinal (GIS) infection in 3 days-6 weeks and evidence of triggering infection. Recently, ReA is classified as SpA and patients who do not fulfill SpA criteria are classified as undifferentiated spondyloarthritis (USpA) according to ASAS/EULAR SpA classification criteria.Objectives:In several case reports which are associated with other infective agents are reported and the definition is extended for some clinicians so that SpA which is occurred after any infection is called as ReA. On the other hand, some researchers still accept the classical definition of ReA. The problem with the heterogeneity of opinions and unstandardized definition of ReA hinders studies about pathogenesis and standardization of treatments. In this study, we aimed to determine the spectrum of the use of the definition of reactive arthritis in publications in PubMed between 2009-2019.Methods:The ReA keyword is searched in PubMed for the years between 2009-2019. 248 different publications have been identified and included in this research. 89 articles, 47 reviews, 108 case reports, 2 guidelines, and 2 editorials reviewed for the definition of ReA.Results:Only 42.7% (106 patients) of these publications meet the classical definition which suggests ReA after only GIS and GUS infections. In 4 (1.6%) of the publications ReA was defined after GIS, GUS and oropharyngeal infections; in 3 (1,2%) of the publications after any bacterial infection; in 9 (3.6%) of the publications after any infection. In 8 (3.2%) of the publications, ReA and USPA was used correspondingly. In 39 (15,7%) of the publications the term agent related, ReA was used without making a general definition for ReA. 79 publications (31,9%) have not defined ReA.According to causative agent and ReA relationship, in 64 (24,6%) general infective agents, in 75 (30,2%) classical agents, in 22 (8,9%) other bacterial agents, in 23 (9,3%) streptococcus, in 10(4%) intravesical BCG, in 6 (2.4%) HIV, in 6 (2.4%) tuberculosis, in 12 (4,8%) clostrudium difficle, in 2 (0.8%) parasites were reported. In 31 (12,5%) of the publications the causative agent for the ReA was unknown, the diagnosis was made clinically.Conclusion:In this study, it is aimed to draw attention terminology intricacy and the need for the standardization of the definition of ReA and USpA. It is clear that to standardize the definition of Rea and USpA is necessary. Between 2009-2019 there are reported cases diagnosed as ReA associated with bacterial infections (especially with Clostridium difficile, streptococcus and tuberculosis infections), and viral infections (by a majority with HIV), and parasitic infections. It is not clear if we need to define them classically or define them as USPA. Another important consideration is the necessity of extended laboratory investigations to find out the real causative agent even if the patient is clinically diagnosed with ReA. The requirement of the differentiation between ReA and USpA must be revealed for therapeutic researches.References:[1]A proposal for the classification of patients for clinical and experimental studies on reactive arthritis. Pacheco-Tena C, Burgos-Vargas R, Vázquez-Mellado J, Cazarín J, Pérez-Díaz JA. J Rheumatol. 1999 Jun;26(6):1338-46.[2]The Assessment of SpondyloArthritis International Society classification criteria for peripheral spondyloarthritis and for spondyloarthritis in general. Rudwaleit M, van der Heijde D, Landewé R, Akkoc N, Brandt J, Chou CT, Dougados M, Huang F, Gu J, Kirazli Y, et al. Ann Rheum Dis. 2011;70:25–31.Disclosure of Interests:None declared

scholarly journals Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19

2021 ◽  
Vol 18 (9) ◽  
pp. 4432
Author(s):  
Ronald Manríquez ◽  
Camilo Guerrero-Nancuante ◽  
Felipe Martínez ◽  
Carla Taramasco
Keyword(s):  
Public Health ◽  
Infectious Diseases ◽  
Preventive Measures ◽  
Weighted Graph ◽  
Real Data ◽  
Sir Model ◽  
Weighted Graphs ◽  
Epidemic Disease ◽  
The Real

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19’s pandemic context.

scholarly journals Kunst kui tundenakkus: Lev Tolstoi kunstidefinitsioon analüütilises perspektiivis / Art as emotional infectiousness: Lev Tolstoy’s definition of art in the analytical perspective

2017 ◽  
Vol 15 (19) ◽  
Author(s):  
Marek Volt
Keyword(s):  
Art Criticism ◽  
Necessary Conditions ◽  
Wide Spectrum ◽  
Religious Knowledge ◽  
Action Mechanisms ◽  
Art Works ◽  
Analytical Perspective ◽  
Anglo American ◽  
Definition Of ◽  
Insight Into

Artiklis käsitlen Lev Tolstoi kunstiteooria retseptsiooni anglo-ameerika esteetikas. Esiteks formuleerin Tolstoi kunstidefinitsiooni ja selle põhimõistete kanoonilise tõlgenduse. Seejärel analüüsin määratlust ekstensionaalse adekvaatsuse alusel, keskendudes nii tavapäraste kui võimalike uute etteheidete paikapidavuse uurimisele. Kolmandaks püstitan küsimuse, kas Tolstoi kunstidefinitsiooni kriitika ekstensionaalse adekvaatsuse alusel on üldse õigustatud. Väidan, et kuigi senistel Tolstoi meta-esteetilise rehabiliteerimise katsetel esineb puuduseid, paljastab Tolstoi kunstiteooria immanentne kriitika – teooria vaagimine eeldustelt, millelt see kritiseerib oponeerivaid teooriaid –, et ekstensionaalsest adekvaatsusest lähtuv kriitika on õigustatud. My article discusses Tolstoy’s theory of art in the context of Anglo-American aesthetics. Although Tolstoy’s What is Art touches upon a very wide spectrum of subjects (the place of art in the world, justification of sacrifices made for completing art works, criticism of previous theories of aesthetics, especially of the theory of beauty, defining of art as the expression of feelings, judging of art as such based on the religious knowledge of the era, action mechanisms of beauty/pleasure-centred art, consequences, conditions of the value of art, the relations between art and science, etc.), it has mainly been examined from the aspects of judging and defining of art.The article focuses on Tolstoy’s definition of art and consists of three notional parts. First, I present the canonical formulation of Tolstoy’s definition of art – something is a work of art if and only if the person, who lives through the feeling(s), causes by external signs that the recipients live through the same feelings. I also present the canonical interpretation of its main concepts – the conditions for creation, transmitting and reception.Second, I have an analytical insight into the criticism of the canonical treatment, displaying and commenting on, but also responding and complementing the presented arguments. The extensional adequacy-based analysis of Tolstoy’s definition of art shows that although it is possible to eliminate some of the typical criticisms, none of the three necessary conditions was necessary by itself, nor were all three of them sufficient when taken together.As Tolstoy’s definition of art has sometimes earned quite serious criticism, then, as my third point, I also examine some possibilities for rehabilitating Tolstoy’s theory of art: whether and in what sense can the extensional adequacy-based analysis of Tolstoy’s definition of art be justified at all? So far, the attempts of meta-aesthetic rehabilitation of Tolstoy (e.g., Mounce centrism) have not achieved the expected result. Furthermore, the immanent criticism of Tolstoy’s theory of art (criticism of the theory, based on the prerequisites it uses to criticize its opposing theories) reveals that the extensional adequacy-based criticism of Tolstoy’s definition of art is justified, but it is not necessarily the only yardstick for the theory.

Removing the Nationality Paradigm from Herodotus’ Histories

2018 ◽  
Vol 10 (2) ◽  
pp. 306-323
Author(s):  
Salvatore Tufano
Keyword(s):  
Case Studies ◽  
Final Section ◽  
Fifth Century ◽  
Test Cases ◽  
Persian Wars ◽  
Classical Definition ◽  
Mixed Language ◽  
Archaic Greece ◽  
The Common ◽  
Definition Of

Abstract The present paper suggests that the recurring appeal to kinship diplomacy undermines a fixed idea of ‘nation’ in Archaic Greece, especially in the first two decades of the fifth century BC. It aims to present a series of test cases in Herodotus that explain why contemporary patterns and theories on ancient ethnicity can hardly explain the totality of the historical spectrum. Blood ties could sometimes fortify ethnic relationships, as in the case of Aristagoras’ mission to Sparta (Hdt. 5.49.3), since the common Greekness could elicit the Spartan to help to the Ionians. In other times, the same blood ties were applied to divine genealogies, and they could also be used to show the feeble devotion of cities like Argos to the Greek cause (7.150.2: Xerxes expects the Argives to join the Persian cause, since they descend from Perses). Habits and traditions, often taken as indicia of national feeling, could be thought of as clues of ancient migrations (so the Trojans became Maxyes in Lybia: 4.191). Even language might not help in justifying ethnic relationships: for instance, the Greeks living in the Scythian Gelonus spoke a mixed language (4.108). These few case studies may shed a different light on the classical definition of Greekness (to hellenikon) in terms of blood, language, cults, and habits, all given by Herodotus (8.144). Far from being a valid label for all the Greeks of the fifth century, this statement owes much to a specific variety of the language of kinship diplomacy. The final section argues for the opportunity to avoid the later and misleading idea of nation when studying Herodotus and the age of the Persian Wars, which are instead characterized by various and contrasting strategies. Greek groups and ethne can be better described as networks of lightly defined communities.

Dust storm episodes at the aerodromes in the Asian part of Russia

2021 ◽  
Vol 2 ◽  
pp. 20-42
Author(s):  
A.R. Ivanova ◽  
◽  
E.N. Skriptunova ◽  
N.I. Komasko ◽  
A.A. Zavialova ◽  
...  
Keyword(s):  
Seasonal Variation ◽  
Dust Storm ◽  
Trajectory Analysis ◽  
Dust Storms ◽  
Strong Wind ◽  
Dust Transport ◽  
Air Masses ◽  
Classical Definition ◽  
Dust Events ◽  
Definition Of

Dust storm episodes at the aerodromes in the Asian part of Russia / Ivanova A.R., Skriptunova E.N., Komasko N.I., Zavialova A.A.// Hydrometeorological Research and Forecasting, 2021, no. 2 (380), pp. 20-42. According to 2001-2020 METAR data, episodes of dust storms at 26 international aerodromes in the Asian Russia causing poor visibility are studied. The conditions for issuing reports on dust storms, their correspondence to the definition of a dust storm are discussed. It was found that out of 337 reports describing dust transport by strong wind, only 7 episodes registered at the aerodromes of Irkutsk, Abakan, Omsk, and Blagoveshchensk corresponded to the classical definition. The others detected at 15 of 26 aerodromes may be defined as “dust events” – the episodes of dust transfer causing the nonessential visibility reduction. The seasonal variation in such episodes and its connection with changes in visibility are studied. The characteristics of dusty air masses and the direction of their advection are given. Keywords: dust storm, dust events, aerodromes of Asian Russia, seasonal variation, trajectory analysis

On Integer Matrices and Incidence Matrices of Certain Combinatorial Configurations, III: Rectangular Matrices

1966 ◽  
Vol 18 ◽  
pp. 9-17
Author(s):  
Kulendra N. Majindar
Keyword(s):  
Necessary Conditions ◽  
Block Designs ◽  
Incomplete Block ◽  
Incidence Matrices ◽  
Balanced Incomplete Block Designs ◽  
Balanced Incomplete Block ◽  
Definition Of ◽  
Combinatorial Configurations

In this paper, we give a connection between incidence matrices of affine resolvable balanced incomplete block designs and rectangular integer matrices subject to certain arithmetical conditions. The definition of these terms can be found in paper II of this series or in (2). For some necessary conditions on the parameters of affine resolvable balanced incomplete block designs and their properties see (2).

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