We analyze the role played by functions with positive differences defined on convex cones. In particular, we study functions that satisfy linear functional inequalities that extend the three-variable ...Hornich-Hlawka functional inequality,
f
x
+
f
y
+
f
z
+
f
x
+
y
+
z
≥
f
x
+
y
+
f
y
+
z
+
f
z
+
x
+
f
(
0
)
,
especially to the case of
n
variables. Beyond the classical setting, we present extensions to the case of positive operators.
Abstract Growing evidence suggests that the arcopallium/posterior pallial amygdala plays a major role in the control of fear behaviour in birds. This brain region comprises several subdivisions, but ...no direct evidence is available about its functional parcellation. The aim of the present study was to investigate the relative involvement of two subdivisions of the arcopallium/posterior pallial amygdala complex in four classical tests of fear in quail: the presentation of a novel object, the ‘hole-in-the-wall’, ‘open-field’ and tonic immobility tests. Bilateral electrolytic lesions damaging the posterior part of the arcopallium/posterior pallial amygdala resulted in an increase in fear behaviour in the ‘open-field’ test, whereas quail with lesions damaging the anterior part of the arcopallium displayed a decrease in an ‘overall fear score’, compared to quail with bilateral nidopallium or sham lesions. The differential involvement of the anterior and posterior parts of the arcopallium/posterior pallial amygdala in fear behaviour is discussed in view of the known connections between the arcopallium/posterior pallial amygdala complex and brain regions considered to be limbic in nature.
► Emotionality trait influences exploratory behaviour in Japanese quail. ► Diazepam decreases impact of emotionality on exploratory behaviour. ► Selection on tonic immobility response represents ...valuable model of bird anxiety.
This study tested whether lines of Japanese quails divergently selected for a fear response, the tonic immobility, might constitute a reliable bird model for studying anxiety. Previous studies demonstrated that the selection modifies the general underlying emotionality of the birds rather than exerting its effect only on tonic immobility. The behavioural effects of intraperitoneal injections of diazepam, an anxiolytic drug, were assessed in two lines of quail selected either for their short (STI) or long (LTI) duration of tonic immobility. Effects of diazepam were examined in two tests used for measuring emotionality in birds, the open field and the tonic immobility tests. After being placed in the centre of the open field, birds with a high emotionality (LTI quails) stayed longer in the centre of the apparatus than STI quail. Diazepam had anxiolytic effect in LTI birds as it increased the time spent in the outer area. This effect of diazepam appears to be selective because the drug has no effect on other behaviours such as distress calls or escape attempts. The drug has also no effect on the tonic immobility response in any of the two lines. These findings reveal an “anxiogenic” trait of LTI birds in the open field test that can be modulated by the administration of an anxiolytic drug. Therefore quails selected for LTI and STI represent a valuable model to study the mechanisms underlying anxiety in birds.
An Extension of Young's Inequality Mitroi, Flavia-Corina; Niculescu, Constantin P.
Abstract and Applied Analysis,
01/2011, Letnik:
2011, Številka:
2011
Journal Article
Recenzirano
Odprti dostop
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.
•High anxiety trait has no effect on object habituation in Japanese quail.•High anxiety trait enhanced object discrimination in Japanese quail.•High anxiety trait is associated with accurate ...processing of environmental cues.
Compared to rodents, the relationship between anxiety and cognitive performances has been less studied in birds. Yet, birds are frequently exposed to stimulations that constitute a potential source of anxiety and can affect their adaptation to their living conditions. The present study was aimed at evaluating, in birds, the relationship between levels of anxiety and object habituation and discrimination with the use of Japanese quail lines divergently selected for a fear response, tonic immobility. Previous studies demonstrated that the selection programme has modified the general anxiety trait of the birds. The task consisted in 4 daily sessions of 8 successive presentations of the same object in the home cage of the quail in order to habituate each bird to the object. The observation that both quail with a high and a low anxiety trait progressively spent more time close to the object indicated that habituation occurred. Dishabituation was assessed during a single session of 8 presentations of a novel object. Only quail with a high anxiety trait exhibited significant discrimination. They spent significantly less time close to the novel object than to the habituated object. It is hypothesised that a high anxiety trait is associated with a more accurate processing of environmental cues or events resulting in better discriminative performances.
One proves that most results known for the usual convex functions (including Jensen's inequality, Jensen's characterization of convexity, the duality between monotone and convex functions, the ...existence of affine supports etc.), have analogs for Popoviciu's convex functions. The details are presented in the case of two variables, but the theory exposed here can be easily extended to higher dimensions.
We study top-down embeddings of massive Anti-de Sitter (AdS) gravity in type-IIB string theory. The supergravity solutions have a AdS$_4$ fiber warped over a manifold M$_6$ whose shape resembles that ...of scottish bagpipes: The `bag' is a conventional AdS$_4$-compactification manifold, while the `pipes' are highly-curved semi-infinite Janus throats. Besides streamlining previous discussions of the problem, our main new result is a formula for the graviton mass which only depends on the effective gravitational coupling of the bag, and on the D3-brane charges and dilaton jumps of the Janus throats. We compare these embeddings to the Karch-Randall model and other bottom-up proposals for massive-AdS-gravity, and we comment on their holographic interpretation. This is a companion paper to 1, where some closely-related bimetric models with pure AdS$_5\times$S$^5$ throats were analyzed.
Band structure in Yang-Mills theories Bachas, Constantin; Tomaras, Theodore
The journal of high energy physics,
05/2016, Letnik:
2016, Številka:
5
Journal Article
Recenzirano
Odprti dostop
A
bstract
We show how Yang-Mills theory on S
3
×
ℝ
can exhibit a spectrum with continuous bands if coupled either to a topological 3-form gauge field, or to a dynamical axion with heavy ...Peccei-Quinn scale. The basic mechanism consists in associating winding histories to a bosonic zero mode whose role is to convert a circle in configuration space into a helix. The zero mode is, respectively, the holonomy of the 3-form field or the axion momentum. In these models different
θ
sectors coexist and are only mixed by (non-local) volume operators. Our analysis sheds light on, and extends Seiberg’s proposal for modifying the topological sums in quantum field theories. It refutes a recent claim that
B
+
L
violation at LHC is unsuppressed.
In
Indiscrete Thoughts
18
, G.-C. Rota remarked, “The mystery, as well as the glory of mathematics, lies not so much in the fact that abstract theories do turn out to be useful in solving problems, ...but, wonder of wonders, in the fact that a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended. These coincidences occur so frequently, that they must belong to the essence of mathematics.” Indeed, it happens often that abstract mathematics leads to concrete applications, and real-life problems constitute a source of inspiration for sophisticated theories. The strong synergy between pure mathematics and its applications advocates for teaching methods that intertwine physical intuition with mathematical abstraction, and recognize the universality of mathematical laws throughout the sciences.
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