1,489 research outputs found
A nilpotent group without local functional equations for pro-isomorphic subgroups
The pro-isomorphic zeta function of a torsion-free finitely generated
nilpotent group G enumerates finite index subgroups H such that H and G have
isomorphic profinite completions. It admits an Euler product decomposition,
indexed by the rational primes. We manufacture the first example of a
torsion-free finitely generated nilpotent group G such that the local Euler
factors of its pro-isomorphic zeta function do not satisfy functional
equations. The group G has nilpotency class 4 and Hirsch length 25. It is
obtained, via the Malcev correspondence, from a Z-Lie lattice L with a suitable
algebraic automorphism group Aut(L).Comment: 16 page
Stationary and regenerative multivariate point processes
Imperial Users onl
On pro-isomorphic zeta functions of -groups of even Hirsch length
Pro-isomorphic zeta functions of finitely generated nilpotent groups form one
of the group-theoretic generalisations of the Riemann zeta functions. They are
Dirichlet generating functions enumerating finite-index subgroups whose
profinite completion is isomorphic to that of the ambient group. We study
pro-isomorphic zeta functions of -groups; these form the building blocks
of finitely generated class two nilpotent groups with centre of rank two, up to
commensurability. These groups were classified by Grunewald and Segal, and can
be indexed by primary polynomials whose companion matrices define commutator
relations. We provide a key step towards the elucidation of the pro-isomorphic
zeta functions of -groups of even Hirsch length by describing the
automorphism groups of the associated graded Lie rings. Utilizing this
description of the automorphism groups, we calculate the local pro-isomorphic
zeta functions of groups associated to the polynomials and . In both
cases, the local zeta functions are uniform in the prime~ and satisfy
functional equations.Comment: 29 page
Uniformity and Functional Equations for Local Zeta Functions of -Split Algebraic Groups
We study the local zeta functions of an algebraic group defined
over together with a faithful -rational
representation for a finite extension of .
These are given by integrals over -adic points of
determined by for a prime of . We prove
that the local zeta functions are almost uniform for all -split
groups whose unipotent radical satisfies a certain lifting property. This
property is automatically satisfied if is reductive. We provide a
further criterion in terms of invariants of and which
guarantees that the local zeta functions satisfy functional equations for
almost all primes of . We obtain these results by using a
-adic Bruhat decomposition of Iwahori and Matsumoto [IM] to
express the zeta function as a weighted sum over the Weyl group associated
to of generating functions over lattice points of a polyhedral
cone. The functional equation reflects an interplay between symmetries of the
Weyl group and reciprocities of the combinatorial object. We construct families
of groups with representations violating our second structural criterion whose
local zeta functions do not satisfy functional equations. Our work generalizes
results of Igusa [Igu] and du Sautoy and Lubotzky [dSL] and has implications
for zeta functions of finitely generated torsion-free nilpotent groups.Comment: 22 page
Thinking beyond health to motivate dietary change: piloting a vegan healthy eating program for obesity management
This pilot study assessed the feasibility, acceptability and efficacy of a novel approach to facilitating dietary change and weight loss in obese adults by presenting vegan environmental, health and farm animal treatment information in a 6 week, group-based, educational nutrition program (called a vegan healthy eating program). Twenty-nine (29) medically stable, obese adults were recruited from 3 ambulatory care clinics at UCSF and enrolled using partial randomization into one of two serially occurring intervention groups (Group 1 n=14, followed by Group 2 n=15). A delayed intervention control group (n=9) was used, consisting of participants enrolled in Group 2 who were available for collection of baseline measures prior to the start of Group 1s intervention. All intervention participants provided data immediately following their vegan healthy eating program (2 months post baseline) and again at 3 and 9 months post baseline. 10% of initial contacts (29 patients) met inclusion and exclusion criteria and were enrolled; 25 participants were retained at 3 months, 20 at 9 months. Mean intervention session satisfaction as measured by anonymous surveys using a 1-7 Likert scale (1=extremely unsatisfied, 7=extremely satisfied) was 6.2 (SD=1.1). Statistically significant reductions in calories from animal products, percent fat, cholesterol and increases in the recommended food score, fruits and vegetable servings were observed within the intervention group only, at all timepoints. Mean weight change was +2.8 lbs (3.0, n=8, p=0.035) in control participants after 4.3 weeks, and -3.4 lbs (5.0, n=25, p=0.002), -5.9 lbs (7.7, n=25, p=0.001), and -8.8 lbs (14.2, n=20, p=0.012) after 7.3, 15.6 and 41.7 weeks in intervention participants, respectively. In conclusion, this vegan healthy eating program demonstrated good feasibility, high satisfaction, and facilitated a shift towards a plant-based diet and modest, progressive short-term weight loss among intervention participants
Interaction of cocaine with some central dopominergic and serotonergic mechanisms
The present study ln male Wistar rats was designed to rate and analyze six specific cocaine-induced behaviors. These behavioral parameters have been defined by others as either dopaminergic (sniffing, grooming, and locomotor activity) or serotonergic (repetitive head movements, rearing, and Straub tail) in origin.
Results were analyzed by analysis of variance in two ways : (i) as grouped dopaminergic or serotonergic scores, and (ii) as the net behavioral index (dopaminergic scores minus the serotonergic scores). The purpose of approaching the data in this way was to attempt to define the behavioral interactions of the two neurotransmitters.
One conclusion that developed from this study was the indication that dopaminergic behaviors peak at lower doses of cocaine than do serotonergic behaviors. This relationship held true for all the individual parameters in addition to the dopaminergic and serotonergic totals.
A dopaminergic blocker, haloperidol, significantly attenuated all responses elicited by cocaine. When the net behavioral index was analyzed, it was found that the response of the median dose of cocaine was significantly altered from a net dopaminergic score towards a net serotonergic score. In this sense, haloperidol was shown to have the capacity to attenuate dopaminergic-associated parameters to a greater extent than the serotonergic-associated parameters.
Cyproheptadine, an antiserotonergic agent, did not significantly affect the net behavioral index; however, this compound did significantly increase the dopaminergic parameter of grooming at the high doses of cocaine and cyproheptadine. Also at this dose combination , gnawing was elicited -- a dopaminergic response seen under no other experimental conditions. Due to the antiserotonergic agent causing an increase in the dopaminergic parameters of grooming and gnawing, it is proposed that the serotonergic influence on these two dopaminergic behaviors is of an inhibitory type
- …