scholarly journals Note on the Union-Closed Sets Conjecture

10.37236/6989 ◽  
2017 ◽  
Vol 24 (3) ◽  
Author(s):  
Abigail Raz
Keyword(s):  
Finite Family ◽  
Closed Sets ◽  
Set Size ◽  
Do So

The union-closed sets conjecture states that if a finite family of sets $\mathcal{A} \neq \{\varnothing\}$ is union-closed, then there is an element which belongs to at least half the sets in $\mathcal{A}$. In 2001, D. Reimer showed that the average set size of a union-closed family, $\mathcal{A}$, is at least $\frac{1}{2} \log_2 |\mathcal{A}|$. In order to do so, he showed that all union-closed families satisfy a particular condition, which in turn implies the preceding bound. Here, answering a question raised in the context of T. Gowers' polymath project on the union-closed sets conjecture, we show that Reimer's condition alone is not enough to imply that there is an element in at least half the sets.

scholarly journals Well-Graded Families and the Union-Closed Sets Conjecture

10.37236/8380 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Jeffrey Matayoshi
Keyword(s):  
Finite Family ◽  
Closed Sets ◽  
The Relationship ◽  
Extra Structure

The union-closed sets conjecture states that if a finite family of sets $\mathcal{F}$ is union-closed, then there must be some element contained in at least half of the sets of $\mathcal{F}$.  In this work we study the relationship between the union-closed sets conjecture and union-closed families that have the property of being well-graded.  In doing so, we show how the density and other properties are affected by the extra structure contained in well-graded families, and we also give several conditions under which well-graded families satisfy the union-closed sets conjecture.

Person organization with a memory set: are spontaneous trait inferences personality characterizations or behaviour labels?

1993 ◽  
Vol 7 (3) ◽  
pp. 195-208 ◽  
Author(s):  
Gordon B. Moskowitz
Keyword(s):  
Impression Formation ◽  
Personality Characteristics ◽  
Current Experiment ◽  
Stimulus Information ◽  
Set Size ◽  
The People ◽  
Spontaneous Trait Inferences ◽  
Trait Inferences ◽  
Set Size Effects ◽  
Do So

Recent research on impression formation has demonstrated that perceivers can categorize the action of target actors in terms of the traits that those behaviours represent, and that they do so in a spontaneous fashion, with neither the intent of categorizing nor the awareness of categorizing. This has resulted in a discussion about what these inferences refer to. Are they simple summaries of the behaviour without implications for the personalities of the people enacting those behaviours, or are they inferences about the target's disposition? The current experiment uses a procedure from the person memory literature to establish that these inferences are in fact references to the qualities of the target actors. Set size effects demonstrate that perceivers are organizing their inferred traits in person nodes; the person serves as the superordinate cue to which inferences are attached. This not only provides evidence that inferences formed spontaneously refer to the personality characteristics of the target, but also provides the first evidence of person organization under simple instructions to memorize stimulus information. The implications of the richness of the target information for spontaneously forming person inferences and for person organization in general are discussed.

scholarly journals Is the Union-closed sets conjecture the best possible?

1991 ◽  
Vol 51 (2) ◽  
pp. 276-283 ◽  
Author(s):  
J. C. Renaud
Keyword(s):  
Boundary Function ◽  
Closed Sets ◽  
Set Size ◽  
Strengthened Version

AbstractA slightly strengthened version of the union-closed sets conjecture is proposed. It is shown that this version holds for a minimum set size of one or two and an examination of a boundary function shows that it holds for collections containing up to 19 sets. Some related conjectures are outlined.

Holding replication studies to mainstream standards of evidence

2018 ◽  
Vol 41 ◽  
Author(s):  
Duane T. Wegener ◽  
Leandre R. Fabrigar
Keyword(s):  
Replication Studies ◽  
Replication Research ◽  
Standards Of Evidence ◽  
Do So

AbstractReplications can make theoretical contributions, but are unlikely to do so if their findings are open to multiple interpretations (especially violations of psychometric invariance). Thus, just as studies demonstrating novel effects are often expected to empirically evaluate competing explanations, replications should be held to similar standards. Unfortunately, this is rarely done, thereby undermining the value of replication research.

Electron Microscopy of a Herpesvirus Isolated from Marek's Disease in Duck and Chicken Embryo Fibroblast Cultures

1968 ◽  
Vol 26 ◽  
pp. 222-223 ◽  
Author(s):  
Keyvan Nazerian
Keyword(s):  
Inclusion Bodies ◽  
Chicken Embryo Fibroblast ◽  
Marek's Disease ◽  
Marek’S Disease ◽  
Duck Embryo Fibroblast ◽  
Multinucleated Cells ◽  
Viral Particles ◽  
Infected Cells ◽  
And Control ◽  
Do So

A herpes-like virus has been isolated from duck embryo fibroblast (DEF) cultures inoculated with blood from Marek's disease (MD) infected birds. Cultures which contained this virus produced MD in susceptible chickens while virus negative cultures and control cultures failed to do so. This and other circumstantial evidence including similarities in properties of the virus and the MD agent implicate this virus in the etiology of MD.Histochemical studies demonstrated the presence of DNA-staining intranuclear inclusion bodies in polykarocytes in infected cultures. Distinct nucleo-plasmic aggregates were also seen in sections of similar multinucleated cells examined with the electron microscope. These aggregates are probably the same as the inclusion bodies seen with the light microscope. Naked viral particles were observed in the nucleus of infected cells within or on the edges of the nucleoplasmic aggregates. These particles measured 95-100mμ, in diameter and rarely escaped into the cytoplasm or nuclear vesicles by budding through the nuclear membrane (Fig. 1). The enveloped particles (Fig. 2) formed in this manner measured 150-170mμ in diameter and always had a densely stained nucleoid. The virus in supernatant fluids consisted of naked capsids with 162 hollow, cylindrical capsomeres (Fig. 3). Enveloped particles were not seen in such preparations.

Debates in Dysphagia Management: How Do You Use Evidence-Based Practice in Your Dysphagia Patient Care?

2011 ◽  
Vol 20 (4) ◽  
pp. 121-123
Author(s):  
Jeri A. Logemann
Keyword(s):  
Decision Making ◽  
Patient Care ◽  
Clinical Outcomes ◽  
Clinical Judgment ◽  
Clinical Decision Making ◽  
Evidence Based Practice ◽  
Clinical Decision ◽  
Evidence Based ◽  
Clinical Method ◽  
Do So

Evidence-based practice requires astute clinicians to blend our best clinical judgment with the best available external evidence and the patient's own values and expectations. Sometimes, we value one more than another during clinical decision-making, though it is never wise to do so, and sometimes other factors that we are unaware of produce unanticipated clinical outcomes. Sometimes, we feel very strongly about one clinical method or another, and hopefully that belief is founded in evidence. Some beliefs, however, are not founded in evidence. The sound use of evidence is the best way to navigate the debates within our field of practice.

Face and Word Recognition in Patients with Left and Right Hemispheric Lesions: Evidence from Reaction Times and ERPs

2002 ◽  
Vol 13 (1) ◽  
pp. 69-83 ◽  
Author(s):  
Stefan R. Schweinberger ◽  
Thomas Klos ◽  
Werner Sommer
Keyword(s):  
Slow Wave ◽  
Reaction Times ◽  
Memory Search ◽  
Event Related Potentials ◽  
Performance Deficits ◽  
Set Size ◽  
Left Brain ◽  
Related Potentials ◽  
Abstract Words ◽  
Left Brain Damage

Abstract: We recorded reaction times (RTs) and event-related potentials (ERPs) in patients with unilateral lesions during a memory search task. Participants memorized faces or abstract words, which were then recognized among new ones. The RT deficit found in patients with left brain damage (LBD) for words increased with memory set size, suggesting that their problem relates to memory search. In contrast, the RT deficit found in patients with RBD for faces was apparently related to perceptual encoding, a conclusion also supported by their reduced P100 ERP component. A late slow wave (720-1720 ms) was enhanced in patients, particularly to words in patients with LBD, and to faces in patients with RBD. Thus, the slow wave was largest in the conditions with most pronounced performance deficits, suggesting that it reflects deficit-related resource recruitment.

The Persnickety Pervasiveness of Rating Enhancement in Personality Assessment

2020 ◽  
pp. 1-13
Author(s):  
Alicia A. Stachowski ◽  
John T. Kulas
Keyword(s):  
Response Bias ◽  
Personality Assessment ◽  
Current Paper ◽  
Psychological Measurement ◽  
Shared Sets ◽  
Self Reports ◽  
Original Target ◽  
Target Profile ◽  
Do So ◽  
Normative Influences

Abstract. The current paper explores whether self and observer reports of personality are properly viewed through a contrasting lens (as opposed to a more consonant framework). Specifically, we challenge the assumption that self-reports are more susceptible to certain forms of response bias than are informant reports. We do so by examining whether selves and observers are similarly or differently drawn to socially desirable and/or normative influences in personality assessment. Targets rated their own personalities and recommended another person to also do so along shared sets of items diversely contaminated with socially desirable content. The recommended informant then invited a third individual to additionally make ratings of the original target. Profile correlations, analysis of variances (ANOVAs), and simple patterns of agreement/disagreement consistently converged on a strong normative effect paralleling item desirability, with all three rater types exhibiting a tendency to reject socially undesirable descriptors while also endorsing desirable indicators. These tendencies were, in fact, more prominent for informants than they were for self-raters. In their entirety, our results provide a note of caution regarding the strategy of using non-self informants as a comforting comparative benchmark within psychological measurement applications.

Training Set Size and Response Location Effects on Same/Different Judgments in Humans

2011 ◽  
Author(s):  
Jeffrey S. Katz ◽  
John F. Magnotti ◽  
Anthony A. Wright
Keyword(s):  
Training Set ◽  
Response Location ◽  
Set Size
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