scholarly journals Longest Monotone Subsequences and Rare Regions of Pattern-Avoiding Permutations

10.37236/6402 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Neal Madras ◽  
Gökhan Yıldırım
Keyword(s):  
Lower Boundary ◽  
Specific Pattern ◽  
Main Diagonal ◽  
Exact Results ◽  
Closed Set ◽  
Lipschitz Continuous ◽  
Unit Square ◽  
Expected Length ◽  
Pattern Avoiding Permutations ◽  
Rare Regions

We consider the distributions of the lengths of the longest monotone and alternating subsequences in classes of permutations of size $n$ that avoid a specific pattern or set of patterns, with respect to the uniform distribution on each such class. We obtain exact results for any class that avoids two patterns of length 3, as well as results for some classes that avoid one pattern of length 4 or more. In our results, the longest monotone subsequences have expected length proportional to $n$ for pattern-avoiding classes, in contrast with the $\sqrt n$ behaviour that holds for unrestricted permutations.  In addition, for a pattern $\tau$ of length $k$, we scale the plot of a random $\tau$-avoiding permutation down to the unit square and study the "rare region", which is the part of the square that is exponentially unlikely to contain any points. We prove that when $\tau_1>\tau_k$, the complement of the rare region is a closed set that contains the main diagonal of the unit square. For the case $\tau_1=k,$ we also show that the lower boundary of the part of the rare region above the main diagonal is a curve that is Lipschitz continuous and strictly increasing on $[0,1]$.

scholarly journals Minibatch Forward-Backward-Forward Methods for Solving Stochastic Variational Inequalities

2021 ◽  
Author(s):  
Radu Ioan Boţ ◽  
Panayotis Mertikopoulos ◽  
Mathias Staudigl ◽  
Phan Tu Vuong
Keyword(s):  
Variational Inequalities ◽  
Extragradient Method ◽  
Almost Sure Convergence ◽  
Optimal Solution ◽  
Stochastic Algorithm ◽  
Stochastic Variational Inequalities ◽  
Forward Algorithm ◽  
Closed Set ◽  
Lipschitz Continuous ◽  
Look Ahead

We develop a new stochastic algorithm for solving pseudomonotone stochastic variational inequalities. Our method builds on Tseng’s forward-backward-forward algorithm, which is known in the deterministic literature to be a valuable alternative to Korpelevich’s extragradient method when solving variational inequalities over a convex and closed set governed by pseudomonotone Lipschitz continuous operators. The main computational advantage of Tseng’s algorithm is that it relies only on a single projection step and two independent queries of a stochastic oracle. Our algorithm incorporates a minibatch sampling mechanism and leads to almost sure convergence to an optimal solution. To the best of our knowledge, this is the first stochastic look-ahead algorithm achieving this by using only a single projection at each iteration.

scholarly journals Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions

2000 ◽  
Vol 61 (17) ◽  
pp. 11552-11568 ◽  
Author(s):  
Ferenc Iglói ◽  
Róbert Juhász ◽  
Heiko Rieger
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Exact Results ◽  
Quantum Spin Chains ◽  
Rare Regions

Diagnostic Concordance Between Categorical and Dimensional Instruments to Assess Personality Disorder in Chronic Fatigue Syndrome

2017 ◽  
Vol 33 (3) ◽  
pp. 158-165
Author(s):  
Natalia Calvo ◽  
Naia Sáez-Francàs ◽  
Sergi Valero ◽  
Jesús Castro-Marrero ◽  
José Alegre Martín ◽  
...  
Keyword(s):  
Personality Disorder ◽  
Chronic Fatigue Syndrome ◽  
Personality Assessment ◽  
Chronic Fatigue ◽  
Specific Pattern ◽  
Harm Avoidance ◽  
Assessment Instrument ◽  
Compulsive Disorder ◽  
Fatigue Syndrome ◽  
Self Transcendence

Abstract. The study examines the relationship between a categorical and a dimensional personality assessment instrument in patients with Chronic Fatigue Syndrome (CFS). A total of 162 CFS patients were included in the study (91.4% women; mean age 47.5 years). All subjects completed the Spanish versions of the Personality Diagnostic Questionnaire-4+ (PDQ-4+) and the Temperament and Character Inventory-Revised (TCI-R). Results: 78 (48.1%) of the patients presented a Personality Disorder (PD), the most frequent being Cluster C, specifically Obsessive-compulsive disorder, followed by Avoidant disorder. PDs showed a specific pattern of correlation with temperament scales. All PD clusters correlated positively with Harm Avoidance and Self-Transcendence, and negatively with Reward Dependence, Self-Directedness, and Cooperativeness. In a logistic regression analysis, Self-Directedness and Cooperativeness predicted PD presence. The findings are consistent with previous studies in non-CFS samples and suggest that the combination of the Temperament and Character dimensions (low Self-Directedness and Cooperativeness and high Harm Avoidance and Self-Transcendence) correlates with PD severity, and that Self-Directedness and Cooperativeness are associated with PD presence in CFS patients. The integration of these two perspectives expands the current comprehension of personality pathology in CFS patients.

Erratum - Frustration in periodic systems : exact results for some 2D ising models

1979 ◽  
Vol 40 (10) ◽  
pp. 1024-1024
Author(s):  
G. André ◽  
R. Bidaux ◽  
J.-P. Carton ◽  
R. Conte ◽  
L. de Seze
Keyword(s):  
Ising Models ◽  
Periodic Systems ◽  
Exact Results

Al-Rasm al-ʿUthmānī: Towards Correct Pronunciation and the Preclusion of Ambiguity

2011 ◽  
Vol 13 (2) ◽  
pp. 201-171
Author(s):  
Nāṣir Al-Dīn Abū Khaḍīr
Keyword(s):  
Specific Pattern ◽  
Writing Style ◽  
The Third ◽  
The Past ◽  
Different Ages ◽  
Correct Pronunciation ◽  
The One ◽  
The Mind

The ʿUthmānic way of writing (al-rasm al-ʿUthmānī) is a science that specialises in the writing of Qur'anic words in accordance with a specific ‘pattern’. It follows the writing style of the Companions at the time of the third caliph, ʿUthmān b. ʿAffān, and was attributed to ʿUthmān on the basis that he was the one who ordered the collection and copying of the Qur'an into the actual muṣḥaf. This article aims to expound on the two fundamental functions of al-rasm al-ʿUthmānī: that of paying regard to the ‘correct’ pronunciation of the words in the muṣḥaf, and the pursuit of the preclusion of ambiguity which may arise in the mind of the reader and his auditor. There is a further practical aim for this study: to show the connection between modern orthography and the ʿUthmānic rasm in order that we, nowadays, are thereby able to overcome the problems faced by calligraphers and writers of the past in their different ages and cultures.

Segment–zero alternations in Galician definite article allomorphy

2020 ◽  
Vol 67 (1) ◽  
pp. 155-170
Author(s):  
Shanti Ulfsbjorninn
Keyword(s):  
Specific Pattern ◽  
Definite Article ◽  
Theoretical Discussion

AbstractGalician presents an intriguing case of opaque phonologically-conditioned definite article allomorphy (PCA). Though Galician features in the general literature on PCA (Nevins 2011), there is a surprising lack of synchronic theoretical discussion of this specific pattern. The data appears to require allomorph selection arranged in a system of Priority (Mascaró 2005; Bonet et al. 2003; 2007). The pattern involves opaque segment ‘deletion’ and resyllabification, where segment deletion counterbleeds allomorph insertion along with morphologically-specific segmental changes. A Strict CV representational reanalysis is proposed in which there is no true allomorphy (no selection between competing underlying morphemes). All the forms are generated from a single underlying form, thereby undercutting PRIORITY.

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

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