scholarly journals Fair Division of a Graph

2017 ◽  
Author(s):  
Sylvain Bouveret ◽  
Katarína Cechlárová ◽  
Edith Elkind ◽  
Ayumi Igarashi ◽  
Dominik Peters
Keyword(s):  
Simple Structure ◽  
Fair Division ◽  
Fair Allocation ◽  
Connected Subgraph ◽  
Solution Concepts ◽  
Accessibility Relation ◽  
Acyclic Graphs ◽  
Special Cases ◽  
Additive Utilities ◽  
The Relationship

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agent's share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases wherethe underlying graph has simple structure, and/or the number of agents---or, less restrictively, the number of agent types---is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently.

scholarly journals Fair Division Under Cardinality Constraints

2018 ◽  
Author(s):  
Arpita Biswas ◽  
Siddharth Barman
Keyword(s):  
Resource Allocation ◽  
Fair Division ◽  
Division Problem ◽  
Fair Allocation ◽  
Indivisible Goods ◽  
Solution Concepts ◽  
Cardinality Constraints ◽  
The Given

We consider the problem of fairly allocating indivisible goods, among agents, under cardinality constraints and additive valuations. In this setting, we are given a partition of the entire set of goods---i.e., the goods are categorized---and a limit is specified on the number of goods that can be allocated from each category to any agent. The objective here is to find a fair allocation in which the subset of goods assigned to any agent satisfies the given cardinality constraints. This problem naturally captures a number of resource-allocation applications, and is a generalization of the well-studied unconstrained fair division problem.  The two central notions of fairness, in the context of fair division of indivisible goods, are envy freeness up to one good (EF1) and the (approximate) maximin share guarantee (MMS). We show that the existence and algorithmic guarantees established for these solution concepts in the unconstrained setting can essentially be achieved under cardinality constraints. Furthermore, focusing on the case wherein all the agents have the same additive valuation, we establish that EF1 allocations exist even under matroid constraints.

scholarly journals Surrogate Endpoint Evaluation: Principal Stratification Criteria and the Prentice Definition

2015 ◽  
Vol 3 (2) ◽  
pp. 157-175 ◽  
Author(s):  
Peter B. Gilbert ◽  
Erin E. Gabriel ◽  
Ying Huang ◽  
Ivan S.F. Chan
Keyword(s):  
Causal Effect ◽  
Surrogate Endpoint ◽  
Effect Modification ◽  
Principal Stratification ◽  
Clinical Endpoint ◽  
Efficacy Trial ◽  
Marker Selection ◽  
Special Cases ◽  
High Utility ◽  
The Relationship

AbstractA common problem of interest within a randomized clinical trial is the evaluation of an inexpensive response endpoint as a valid surrogate endpoint for a clinical endpoint, where a chief purpose of a valid surrogate is to provide a way to make correct inferences on clinical treatment effects in future studies without needing to collect the clinical endpoint data. Within the principal stratification framework for addressing this problem based on data from a single randomized clinical efficacy trial, a variety of definitions and criteria for a good surrogate endpoint have been proposed, all based on or closely related to the “principal effects” or “causal effect predictiveness (CEP)” surface. We discuss CEP-based criteria for a useful surrogate endpoint, including (1) the meaning and relative importance of proposed criteria including average causal necessity (ACN), average causal sufficiency (ACS), and large clinical effect modification; (2) the relationship between these criteria and the Prentice definition of a valid surrogate endpoint; and (3) the relationship between these criteria and the consistency criterion (i.e. assurance against the “surrogate paradox”). This includes the result that ACN plus a strong version of ACS generally do not imply the Prentice definition nor the consistency criterion, but they do have these implications in special cases. Moreover, the converse does not hold except in a special case with a binary candidate surrogate. The results highlight that assumptions about the treatment effect on the clinical endpoint before the candidate surrogate is measured are influential for the ability to draw conclusions about the Prentice definition or consistency. In addition, we emphasize that in some scenarios that occur commonly in practice, the principal strata subpopulations for inference are identifiable from the observable data, in which cases the principal stratification framework has relatively high utility for the purpose of effect modification analysis and is closely connected to the treatment marker selection problem. The results are illustrated with application to a vaccine efficacy trial, where ACN and ACS for an antibody marker are found to be consistent with the data and hence support the Prentice definition and consistency.

scholarly journals Addition Formula and Related Integral Equations for Heine—Stieltjes Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1231
Author(s):  
Hans Volkmer
Keyword(s):  
Integral Equations ◽  
Explicit Form ◽  
Spherical Harmonics ◽  
Reproducing Kernel ◽  
Addition Formula ◽  
Symmetric Products ◽  
Special Cases ◽  
Related Integral ◽  
Generalized Spherical Harmonics ◽  
The Relationship

It is shown that symmetric products of Heine–Stieltjes quasi-polynomials satisfy an addition formula. The formula follows from the relationship between Heine–Stieltjes quasi-polynomials and spaces of generalized spherical harmonics, and from the known explicit form of the reproducing kernel of these spaces. In special cases, the addition formula is written out explicitly and verified. As an application, integral equations for Heine–Stieltjes quasi-polynomials are found.

An analysis of the variation between dairy-sire progeny-groups for milk yield and fat content

1958 ◽  
Vol 1958 ◽  
pp. 19-29 ◽  
Author(s):  
Alan Robertson ◽  
S. S. Khishin
Keyword(s):  
Milk Yield ◽  
Comparison Method ◽  
Fat Content ◽  
Fat Percentage ◽  
Simple Method ◽  
Factors Affecting ◽  
Special Cases ◽  
The Mean ◽  
Milk Marketing ◽  
The Relationship

The past few years have seen the development in Great Britain of the ‘contemporary comparison’ method for evaluating progeny tests of dairy sires (Macarthur, 1954; Robertson, Stewart and Ashton 1956). The final overall figure attached to a sire is the mean difference between the yield of his daughters and that of other heifers milking in the same herd in the same year, with due regard for the numbers of animals in the two groups. Although it has some imperfections in special cases, this is probably the most informative simple method of evaluating a sire for yield and, fortunately, one which could be easily integrated with the existing recording system. The method has been turned into a simple routine in the Bureau of Records of the Milk Marketing Board and several thousand bulls have now been evaluated. In this paper, we shall be mostly concerned to use this material to investigate the heritabilities of milk yield and fat content and the relationship between the two in the different breeds. The information that we shall use consists, for each bull, of the mean contemporary comparison, with its effective ‘weight’, and the average fat percentage of the daughters. Before we deal with the observed results, we should go into rather more detail into the nature of these two figures and into the factors affecting them.

scholarly journals Bounding Uncertainty for Active Batch Selection

2019 ◽  
Vol 33 ◽  
pp. 5240-5247 ◽  
Author(s):  
Hanmo Wang ◽  
Runwu Zhou ◽  
Yi-Dong Shen
Keyword(s):  
Objective Function ◽  
Classification Accuracy ◽  
State Of The Art ◽  
Batch Mode ◽  
Initial Stage ◽  
Special Cases ◽  
Testing Data ◽  
The Relationship ◽  
Representative Samples ◽  
Screening Approaches

The success of batch mode active learning (BMAL) methods lies in selecting both representative and uncertain samples. Representative samples quickly capture the global structure of the whole dataset, while the uncertain ones refine the decision boundary. There are two principles, namely the direct approach and the screening approach, to make a trade-off between representativeness and uncertainty. Although widely used in literature, little is known about the relationship between these two principles. In this paper, we discover that the two approaches both have shortcomings in the initial stage of BMAL. To alleviate the shortcomings, we bound the certainty scores of unlabeled samples from below and directly combine this lower-bounded certainty with representativeness in the objective function. Additionally, we show that the two aforementioned approaches are mathematically equivalent to two special cases of our approach. To the best of our knowledge, this is the first work that tries to generalize the direct and screening approaches. The objective function is then solved by super-modularity optimization. Extensive experiments on fifteen datasets indicate that our method has significantly higher classification accuracy on testing data than the latest state-of-the-art BMAL methods, and also scales better even when the size of the unlabeled pool reaches 106.

scholarly journals PARABOLIC KAZHDAN–LUSZTIG BASIS, SCHUBERT CLASSES, AND EQUIVARIANT ORIENTED COHOMOLOGY

2019 ◽  
Vol 19 (6) ◽  
pp. 1889-1929
Author(s):  
Cristian Lenart ◽  
Kirill Zainoulline ◽  
Changlong Zhong
Keyword(s):  
Cohomology Ring ◽  
Flag Varieties ◽  
Special Cases ◽  
Oriented Cohomology ◽  
Schubert Classes ◽  
New Interpretation ◽  
The Moment ◽  
The Right ◽  
Relationship Of ◽  
The Relationship

We study the equivariant oriented cohomology ring $\mathtt{h}_{T}(G/P)$ of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and then prove that the respective Bott–Samelson classes in $\mathtt{h}_{T}(G/P)$ can be obtained by applying this action to the fundamental class of the identity point, hence generalizing previously known results of Chow groups by Brion, Knutson, Peterson, Tymoczko and others. Our main result concerns the equivariant oriented cohomology theory $\mathfrak{h}$ corresponding to the 2-parameter Todd genus. We give a new interpretation of Deodhar’s parabolic Kazhdan–Lusztig basis, i.e., we realize it as some cohomology classes (the parabolic Kazhdan–Lusztig (KL) Schubert classes) in $\mathfrak{h}_{T}(G/P)$. We make a positivity conjecture, and a conjecture about the relationship of such classes with smoothness of Schubert varieties. We also prove the latter in several special cases.

scholarly journals NUTRITION OF THE HOST AND NATURAL RESISTANCE TO INFECTION

1949 ◽  
Vol 89 (5) ◽  
pp. 529-539 ◽  
Author(s):  
Howard A. Schneider
Keyword(s):  
Inbred Mouse ◽  
Natural Resistance ◽  
Single Infection ◽  
Mouse Strains ◽  
Time Interval ◽  
Special Cases ◽  
Resistance To Infection ◽  
Relationship Of ◽  
First Time ◽  
The Relationship

The double strain inoculation (DSI) method of testing for natural resistance to infection has been examined in the instance of mouse salmonellosis. The DSI method has been found capable of detecting differences in natural resistance due to genetic as well as nutritional causes. A difference in response to Salmonella infection was found for the first time between the two "susceptible" inbred mouse strains, BSVR and BSVS. Whereas BSVS mice for the most part survived an intraperitoneal injection of 103 "avirulent" S. typhimurium, BSVR mice all succumbed. The relationship of the DSI test to the usual single infection test has been discussed and it is suggested that such single infection tests are special cases of the DSI test, since they involve a heterogeneous bacterial population which can be considered as a mixture of cultures of differing virulence and in which, by a single injection, the usual time interval between the two injections of the DSI method has been reduced to 0.

scholarly journals Space race functional responses

2015 ◽  
Vol 282 (1801) ◽  
pp. 20142121 ◽  
Author(s):  
Henrik Sjödin ◽  
Åke Brännström ◽  
Göran Englund
Keyword(s):  
Functional Response ◽  
Community Dynamics ◽  
Simple Structure ◽  
Functional Responses ◽  
Response Models ◽  
Predator Prey ◽  
Prey System ◽  
Space Race ◽  
Functional Response Models ◽  
The Relationship

We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis–Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka–Volterra predator–prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats.

scholarly journals When Do Envy-Free Allocations Exist?

2019 ◽  
Vol 33 ◽  
pp. 2109-2116 ◽  
Author(s):  
Pasin Manurangsi ◽  
Warut Suksompong
Keyword(s):  
Phase Transition ◽  
High Probability ◽  
Fair Division ◽  
The Other ◽  
Other Hand ◽  
Additive Utilities ◽  
The One

We consider a fair division setting in which m indivisible items are to be allocated among n agents, where the agents have additive utilities and the agents’ utilities for individual items are independently sampled from a distribution. Previous work has shown that an envy-free allocation is likely to exist when m = Ω (n log n) but not when m = n + o (n), and left open the question of determining where the phase transition from non-existence to existence occurs. We show that, surprisingly, there is in fact no universal point of transition— instead, the transition is governed by the divisibility relation between m and n. On the one hand, if m is divisible by n, an envy-free allocation exists with high probability as long as m ≥ 2n. On the other hand, if m is not “almost” divisible by , an envy-free allocation is unlikely to exist even when m = Θ(n log n)/log log n).

scholarly journals A case study and proposal for publishing directed acyclic graphs: The effectiveness of the quadrivalent HPV vaccine in perinatally HIV exposed girls

2021 ◽  
Author(s):  
Ruby Barnard-Mayers ◽  
Hiba Kouser ◽  
Jamie A. Cohen ◽  
Katherine Tassiopoulos ◽  
Ellen C. Caniglia ◽  
...  
Keyword(s):  
Hpv Vaccine ◽  
Directed Acyclic Graphs ◽  
Hiv Status ◽  
Causal Graph ◽  
Acyclic Graphs ◽  
Causal Graphs ◽  
Hiv Exposed ◽  
Living With Hiv ◽  
The Relationship

Background: Developing a causal graph is an important step in etiologic research planning and can be used to highlight data flaws and irreparable bias and confounding. Recent findings have suggested that the human papillomavirus (HPV) vaccine is less effective in protection against HPV associated disease in a population of girls living with HIV. Development: In order to understand the relationship between HIV status and HPV vaccine effectiveness, it is important to outline the key assumptions of the causal mechanisms before designing a study to investigate the effect of the HPV vaccine in girls living with HIV infection. Application: We present a causal graph to describe our assumptions and proposed approach to explore this relationship. We hope to obtain feedback on our assumptions prior to data analysis and exemplify the process for designing an etiologic study.Conclusion: The approach we lay out in this paper may be useful for other researchers who have an interest in using causal graphs to describe and assess assumptions in their own research prior to undergoing data collection and/or analysis.

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