Characterization of higher-order monotonicity via integral inequalities

2010 ◽  
Vol 140 (4) ◽  
pp. 723-736 ◽  
Author(s):  
Mihály Bessenyei ◽  
Zsolt Páles
Keyword(s):  
Continuous Function ◽  
Higher Order ◽  
Integral Inequalities ◽  
Monotone Functions ◽  
Hadamard Inequality ◽  
Left Hand ◽  
Right Hand ◽  
Compact Subinterval

The Hermite-Hadamard inequality not only is a consequence of convexity but also characterizes it: if a continuous function satisfies either its left-hand side or its right-hand side on each compact subinterval of the domain, then it is necessarily convex. The aim of this paper is to prove analogous statements for the higher-order extensions of the Hermite-Hadamard inequality. The main tools of the proofs are smoothing by convolution and the support properties of higher-order monotone functions.

scholarly journals Some Inequalities for Stop-Loss Premiums

1977 ◽  
Vol 9 (1-2) ◽  
pp. 75-83 ◽  
Author(s):  
H. Bühlmann ◽  
B. Gagliardi ◽  
H. U. Gerber ◽  
E. Straub
Keyword(s):  
Continuous Function ◽  
Random Variable ◽  
Left Hand ◽  
Right Hand ◽  
Image Position ◽  
The Right ◽  
Stop Loss

In this paper any given risk S (a random variable) is assumed to have a (finite or infinite) mean. We enforce this by imposing E[S−] < ∞.Let then v(t) be a twice differentiate function withand let z be a constant with o ≤ z ≤ 1.We define the premium P as followsor equivalentlyNotation: v−(∞) = ∞.The definitions (1) and (equivalently) (2) are meaningful because of theLemma: a) E[v(S − zQ)] exists for all Q∈(− ∞, + ∞).b) The set{Q∣ − ∞ < Q < + ∞, E[v(S−zQ)]>v((1−z)Q)} is not empty.Proof: a) b) Because of a) E[v(S−zQ)] is always finite or equal to + ∞ If v(− ∞) = − ∞ then E[v(S − zQ)] > v((1 − z)Q) is satisfied for sufficiently small Q. The left hand side of the inequality is a nonincreasing continuous function in P (strictly decreasing if z > 0), while the right hand side is a nondecreasing continuous function in Q (strictly increasing if z > 1).If v(− ∞) = c finite then E[v(S − zQ)] > c(otherwise S would need to be equal to − ∞ with probability 1) and again E[v(S − zQ)] > v((1 − z)Q) is satisfied for sufficiently small Q.

Editorial Note

1946 ◽  
Vol 11 (1) ◽  
pp. 2-2
Keyword(s):  
Editorial Note ◽  
Speech Sounds ◽  
Left Hand ◽  
Hand Column ◽  
Right Hand ◽  
Infant Speech ◽  
The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

Alive Still

2019 ◽  
Author(s):  
Cathy Curtis
Keyword(s):  
New York ◽  
Modern Art ◽  
Severe Form ◽  
The Other ◽  
Left Hand ◽  
Right Hand ◽  
The 1950S ◽  
Village Voice

In 1942, at age twenty, after a vision-impaired and rebellious childhood in Richmond, Virginia, Nell Blaine decamped for New York. Operations had corrected her eyesight, and she was newly aware of modern art, so different from the literal style of her youthful drawings. In Manhattan, she met rising young artists and poets. Her life was hectic, with raucous parties in her loft, lovers of both sexes, and freelance design jobs, including a stint at the Village Voice. Initially drawn to the rigorous formalism of Piet Mondrian, she received critical praise for her jazzy abstractions. During the 1950s, she began to paint interiors and landscapes. By 1959, when the Whitney Museum purchased one of her paintings, her career was firmly established. That year, she contracted a severe form of polio on a trip to Greece; suddenly, she was a paraplegic. Undaunted, she taught herself to paint in oil with her left hand, reserving her right hand for watercolors. In her postpolio work, she achieved a freer style, expressive of the joy she found in flowers and landscapes. Living half the year in Gloucester, Massachusetts, and the other half in New York, she took special delight in painting the views from her windows and from her country garden. Critics found her new style irresistible, and she had a loyal circle of collectors; still, she struggled to earn enough money to pay the aides who made her life possible. At her side for her final twenty-nine years was her lover, painter Carolyn Harris.

scholarly journals Digit Variability in Carotenoid Scores Obtained with the Veggie Meter: A Pilot Study (P02-001-19)

2019 ◽  
Vol 3 (Supplement_1) ◽  
Author(s):  
Velarie Ansu ◽  
Stephanie Dickinson ◽  
Alyce Fly
Keyword(s):  
Indiana University ◽  
Left Hand ◽  
Funding Sources ◽  
Right Hand ◽  
Period Data ◽  
The Mean ◽  
The Right ◽  
Post Hoc ◽  
Main Effects ◽  
Mean Square Errors

Abstract Objectives To determine which digit and hand have the highest and lowest skin carotenoid scores, to compare inter-and-intra-hand variability of digits, and to determine if results are consistent with another subject. Methods Two subjects’ first(F1), second(F2), third(F3) and fifth(F5) digits on both hands were measured for skin carotenoids with a Veggie Meter, for 3 times on each of 18 days over a 37-day period. Data were subjected to ANOVA in a factorial treatment design to determine main effects for hand (2 levels), digits (4), and days (18) along with interactions. Differences between digits were determined by Tukey's post hoc test. Results There were significant hand x digit, hand x day, digit x day, and hand x digit x day interactions and significant simple main effects for hand, digit, and day (all P < 0.001). Mean square errors were 143.67 and 195.62 for subject A and B, respectively, which were smaller than mean squares for all main effects and interactions. The mean scores ± SD for F1, F2, F3, and F5 digits for the right vs left hands for subject A were F1:357.13 ± 45.97 vs 363.74 ± 46.94, F2:403.17 ± 44.77 vs. 353.20 ± 44.13, F3:406.76 ± 43.10 vs. 357.11 ± 45.13, and F5:374.95 ± 53.00 vs. 377.90 ± 47.38. For subject B, the mean scores ± SD for digits for the right vs left hands were F1:294.72 ± 61.63 vs 280.71 ± 52.48, F2:285.85 ± 66.92 vs 252.67 ± 67.56, F3:268.56 ± 57.03 vs 283.22 ± 45.87, and F5:288.18 ± 34.46 vs 307.54 ± 40.04. The digits on the right hand of both subjects had higher carotenoid scores than those on the left hands, even though subjects had different dominant hands. Subject A had higher skin carotenoid scores on the F3 and F2 digits for the right hand and F5 on the left hand. Subject B had higher skin carotenoid scores on F5 (right) and F1 (left) digits. Conclusions The variability due to hand, digit, and day were all greater than that of the 3 replicates within the digit-day for both volunteers. This indicates that data were not completely random across the readings when remeasuring the same finger. Different fingers displayed higher carotenoid scores for each volunteer. There is a need to conduct a larger study with more subjects and a range of skin tones to determine whether the reliability of measurements among digits of both hands is similar across the population. Funding Sources Indiana University.

scholarly journals A closed-loop optogenetic screen for neurons controlling feeding in Drosophila

2021 ◽  
Author(s):  
Celia K S Lau ◽  
Meghan Jelen ◽  
Michael D Gordon
Keyword(s):  
Drosophila Melanogaster ◽  
Expression Pattern ◽  
Sensory Neurons ◽  
Closed Loop ◽  
Higher Order ◽  
Taste Detection ◽  
Proof Of Principle ◽  
Feeding Circuits

Abstract Feeding is an essential part of animal life that is greatly impacted by the sense of taste. Although the characterization of taste-detection at the periphery has been extensive, higher order taste and feeding circuits are still being elucidated. Here, we use an automated closed-loop optogenetic activation screen to detect novel taste and feeding neurons in Drosophila melanogaster. Out of 122 Janelia FlyLight Project GAL4 lines preselected based on expression pattern, we identify six lines that acutely promote feeding and 35 lines that inhibit it. As proof of principle, we follow up on R70C07-GAL4, which labels neurons that strongly inhibit feeding. Using split-GAL4 lines to isolate subsets of the R70C07-GAL4 population, we find both appetitive and aversive neurons. Furthermore, we show that R70C07-GAL4 labels putative second-order taste interneurons that contact both sweet and bitter sensory neurons. These results serve as a resource for further functional dissection of fly feeding circuits.

Upper Extremity Motor Fatigability as an Early Indicator in Pediatric Onset Multiple Sclerosis

2021 ◽  
pp. 088307382199988
Author(s):  
Giuseppina Pilloni ◽  
Martin Malik ◽  
Raghav Malik ◽  
Lauren Krupp ◽  
Leigh Charvet
Keyword(s):  
Multiple Sclerosis ◽  
Grip Strength ◽  
Upper Extremity ◽  
Static Fatigue ◽  
Healthy Controls ◽  
Fatigue Index ◽  
Left Hand ◽  
Right Hand ◽  
Computer Based ◽  
Pediatric Onset

Aim: To adopt a computer-based protocol to assess grip fatigability in patients with pediatric-onset multiple sclerosis to provide detection of subtle motor involvement identifying those patients most at risk for future decline. Method: Pediatric-onset multiple sclerosis patients were recruited during routine outpatient visits to complete a grip assessment and compared to a group of healthy age- and sex-matched controls. All participants completed a computer-based measurement of standard maximal grip strength and repetitive and sustained grip performance measured by dynamic and static fatigue indices. Results: A total of 38 patients with pediatric-onset multiple sclerosis and 24 healthy controls completed the grip protocol (right-hand dominant). There were no significant group differences in maximal grip strength bilaterally (right: 21.8 vs 19.9 kg, P = .25; left: 20.4 vs 18.7 kg, P = .33), although males with pediatric-onset multiple sclerosis were significantly less strong than healthy controls (right: 26.53 vs 21.23 kg, P = .009; left; 25.13 vs 19.63 kg, P = .003). Both dynamic and static fatigue indices were significantly higher bilaterally in pediatric-onset multiple sclerosis compared with healthy control participants (left-hand dynamic fatigue index: 18.6% vs 26.7%, P = .003; right-hand static fatigue index: 28.3% vs 41.3%, P < .001; left-hand static fatigue index: 31.9% vs 42.6%, P < .001). Conclusion: Brief repeatable grip assessment including measures of dynamic and sustained static output can be a sensitive indicator of upper extremity motor involvement in pediatric-onset multiple sclerosis, potentially identifying those in need of intervention to prevent future disability.

scholarly journals Examination and Comparison of Theta Band Connectivity in Left- and Right-Hand Dominant Individuals throughout a Motor Skill Acquisition

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 728
Author(s):  
Jessica McDonnell ◽  
Nicholas P Murray ◽  
Sungwoo Ahn ◽  
Stefan Clemens ◽  
Erik Everhart ◽  
...  
Keyword(s):  
Skill Acquisition ◽  
Information Integration ◽  
Visual Information ◽  
Parietal Lobe ◽  
The United States ◽  
Alternative Methods ◽  
Population Difference ◽  
Left Hand ◽  
Right Hand ◽  
Neurological Differences

The majority of the population identifies as right-hand dominant, with a minority 10.6% identifying as left-hand dominant. Social factors may partially skew the distribution, but it remains that left-hand dominant individuals make up approximately 40 million people in the United States alone and yet, remain underrepresented in the motor control literature. Recent research has revealed behavioral and neurological differences between populations, therein overturning assumptions of a simple hemispheric flip in motor-related activations. The present work showed differentially adaptable motor programs between populations and found fundamental differences in methods of skill acquisition highlighting underlying neural strategies unique to each population. Difference maps and descriptive metrics of coherent activation patterns showed differences in how theta oscillations were utilized. The right-hand group relied on occipital parietal lobe connectivity for visual information integration necessary to inform the motor task, while the left-hand group relied on a more frontal lobe localized cognitive based approach. The findings provide insight into potential alternative methods of information integration and emphasize the importance for inclusion of the left-hand dominant population in the growing conceptualization of the brain promoting the generation of a more complete, stable, and accurate understanding of our complex biology.

scholarly journals A characterization of a map whose inverse limit is an arc

2021 ◽  
pp. 1-17
Author(s):  
SINA GREENWOOD ◽  
SONJA ŠTIMAC
Keyword(s):  
Continuous Function ◽  
Inverse Limit ◽  
Splitting Sequence

Abstract For a continuous function $f:[0,1] \to [0,1]$ we define a splitting sequence admitted by f and show that the inverse limit of f is an arc if and only if f does not admit a splitting sequence.

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