319 research outputs found
Hyperforests on the Complete Hypergraph by Grassmann Integral Representation
We study the generating function of rooted and unrooted hyperforests in a
general complete hypergraph with n vertices by using a novel Grassmann
representation of their generating functions. We show that this new approach
encodes the known results about the exponential generating functions for the
different number of vertices. We consider also some applications as counting
hyperforests in the k-uniform complete hypergraph and the one complete in
hyperedges of all dimensions. Some general feature of the asymptotic regimes
for large number of connected components is discussed.Comment: 35 page
A fermionic field theory for spanning hyperforests
Il modello di Potts generalizza il modello di
Ising del ferromagnetismo assumendo che le variabili di spin possano
assumere q stati distinti. L'interazione tra i primi vicini è a
due soli valori a seconda che questi si trovino nello stesso stato o
in stati differenti.
Nonostante questo modello abbia ricevuto inizialmente poca attenzione,
fin dagli anni '70 è stato oggetto di grande interesse a seguito del
suo ricco comportamento critico e dei suoi stretti legami con alcuni
problemi di statistica su reticolo, di combinatoria e di teoria dei
grafi.
Nel 1972 Fortuin e Kasteleyn mostrarono che è
possibile estendere la definizione del modello di Potts anche a valori
di q non interi. Nel caso in cui l'interazione sia esclusivamente
ferromagnetica, questa estensione definisce una misura di
probabilità, nota con il nome di random-cluster model, che include come caso particolare (q=1) il già noto modello di percolazione.
In questa tesi considereremo in particolar modo il limite q -> 0
del modello di Potts. Questo caso limite ha un
particolare significato combinatorio, infatti la funzione di
partizione del modello di Potts corrisponde per q -> 0 alla
funzione generatrice delle foreste massimali sul grafo in cui il
modello è definito.
Il limite q -> 0 del modello di Potts acquista ulteriore interesse
a seguito della recente scoperta per cui esso
può essere descritto da una teoria fermionica contenente un termine
Gaussiano e uno speciale accoppiamento a quattro fermioni. Questa
teoria fermionica risulta essere equivalente, ad ogni ordine
perturbativo, al modello O(N) prolungato analiticamente a N = -1 e
ad un modello sigma non lineare con gruppo di (super) simmetria OSP(1|2).
Questa corrispondenza, seppur perturbativa, ci segnala che, in due
dimensioni, questa teoria è asintoticamente libera come gran parte
dei modelli sigma non-lineari e le teorie di gauge non-abeliane in
quattro dimensioni.
In questo lavoro viene sviluppata un estensione della teoria
fermionica sopracitata al caso in cui siano presenti interazioni a
più corpi.
Generalizzando opportunamente il modello di Potts per includere tali
interazioni, si mostra come nel limite q -> 0 la funzione di
partizione di questo modello si riconduca alla funzione generatrice
delle iperforeste massimali sull'ipergrafo definito dall'interazione a
più corpi. Viene quindi formulata in termini di variabili di
Grassmann una teoria fermionica che descrive tali oggetti combinatori.
Successivamente questa teoria viene studiata nell'ipotesi che le
interazioni formino un ipergrafo completo. In questo caso, che
fisicamente corrisponde ad una teoria di campo medio, il modello è
esattamente risolubile e la funzione di partizione può essere
calcolata esplicitamente. Ciò costituisce di per sé un risultato
di interesse combinatorio in quanto fornisce il conteggio delle
iperforeste massimali sull'ipergrafo completo.
Si mostra infine questa teoria sia anch'essa in corrispondenza (sempre
perturbativa) con un modello sigma non lineare con supersimmetria OSP(1|2). Viene osservato come la supersimmetria del modello
\sigma non lineare induca nella teoria puramente fermionica una
super-simmetria non manifesta e come questa sia in relazione con
l'algebra dei prodotti scalari per N = -1
The risk of musculoskeletal disorders due to repetitive movements of upper limbs for workers employed in hazelnut sorting
In the agro-industrial sector there are many activities whose urgent rhythms can cause a considerable exposure to bio-mechanical risk factors. In the hazelnut sorting, the workers are subject to several biomechanical risks, with repetitive movements, and operations that require a remarkable degree of strength. A thorough study of the workers' exposure to repetitive manual movements has been carried out, with the aim of setting up the necessary measures to reduce the risk factors. The aim of the research is to assess the risk of work-related musculo-skeletal disorders (WMSDs) due to repetitive work, for workers employed to hazelnut shells sorting. The research was carried out in an agricultural cooperative in the Viterbo's area. For risk assessment authors used a method (Occupational Repetitive Actions "OCRA" index according to ISO 11228- 3:2009, Ergonomics - Manual handling - Part 3: Handling of low loads at high frequency) which keeps into consideration several risk factors (such as repetitiveness, prehension force, posture). The risk was assessed for 16 female workers (in eight workplaces and in two different shifts) through this classification: workers with experience less than 1 year, from 1 to 10 years and more than 10 years. This classification is very important for knowing if the professional experience could be considered a "prevention measure" for the risk reduction. The results show a high risk level for the right and left limb. The factors which more have contributed to reach such risk level are the great number of movements and the lack of recovering time
A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings
Combining tree decomposition and transfer matrix techniques provides a very
general algorithm for computing exact partition functions of statistical models
defined on arbitrary graphs. The algorithm is particularly efficient in the
case of planar graphs. We illustrate it by computing the Potts model partition
functions and chromatic polynomials (the number of proper vertex colourings
using Q colours) for large samples of random planar graphs with up to N=100
vertices. In the latter case, our algorithm yields a sub-exponential average
running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the
exponential running time ~ exp(0.245 N) provided by the hitherto best known
algorithm. We study the statistics of chromatic roots of random planar graphs
in some detail, comparing the findings with results for finite pieces of a
regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded.
Version 3 shows that the worst-case running time is sub-exponential in the
number of vertice
Granulicatella adiacens and Abiotrophia defectiva Native Vertebral Osteomyelitis: Three Cases and Literature Review of Clinical Characteristics and Treatment Approach
Granulicatella adiacens and Abiotrophia defectiva are an increasingly recognized cause of osteoarticular infections. We describe two cases of G. adiacens and one case of A. defectiva native vertebral osteomyelitis (NVO) and review all published cases. Nine cases of G. adiacens NVO and two cases of A. defectiva NVO were previously described. Patients were usually middle-aged men, and classical risk factors for NVO were present in half of the cases. Concomitant bacteremia was reported in 78.6% of cases, and concurrent infective endocarditis occurred in 36.4% of this sub-group of patients. Many different antibiotic schemes were recorded, with median treatment duration of 6weeks. In the most recent reports, glycopeptides represented the most frequent empirical therapy, possibly due to the increasing emergence of G. adiacens and A. defectiva penicillin-resistant strains. Stabilization surgery was rarely required (14.3% of cases), and clinical cure was generally achieved. In conclusion, Granulicatella spp. and Abiotrophia spp. NVO is rare but increasingly described. A total antibiotic course of six weeks seems to be appropriate for noncomplicated cases, and clinical outcome is generally favorable
Leukocyte Integrin Antagonists as a Novel Option to Treat Dry Age-Related Macular Degeneration
Age-related macular degeneration (AMD) is a complex multifactorial degenerative disease
that leads to irreversible blindness. AMD affects the macula, the central part of the retina
responsible for sharp central vision. Retinal pigment epithelium (RPE) is the main cellular
type affected in dry AMD. RPE cells form a monolayer between the choroid and the
neuroretina and are in close functional relationship with photoreceptors; moreover, RPE
cells are part of the blood retina barrier that is disrupted in ocular diseases such as AMD.
During ocular inflammation lymphocytes and macrophages are recruited, contact RPE and
produce pro-inflammatory cytokines, which play an important role in AMD pathogenesis.
The interaction between RPE and immune cells is mediated by leukocyte integrins,
heterodimeric transmembrane receptors, and adhesion molecules, including VCAM-1
and ICAM-1. Within this frame, this study aimed to characterize RPE-leukocytes
interaction and to investigate any potentially beneficial effects induced by integrin
antagonists (DS-70, MN27 and SR714), developed in previous studies. ARPE-19 cells
were co-cultured for different incubation times with Jurkat cells and apoptosis and
necrosis levels were analyzed by flow cytometry. Moreover, we measured the mRNA
levels of the pro-inflammatory cytokine IL-1\u3b2 and the expression of adhesion molecules
VCAM-1 and ICAM-1. We found that RPE-lymphocyte interaction increased apoptosis
and necrosis levels in RPE cells and the expression of IL-1\u3b2. This interaction was mediated
by the binding of \u3b14\u3b21 and \u3b1L\u3b22 integrins to VCAM-1 and ICAM-1, respectively. The
blockade of RPE-lymphocyte interaction with blocking antibodies highlighted the pivotal
role played by integrins. Therefore, \u3b14\u3b21 and \u3b1L\u3b22 integrin antagonists were employed to
disrupt RPE-lymphocyte crosstalk. Small molecule integrin antagonists proved to be
effective in reducing RPE cell death and expression of IL-1\u3b2, demonstrating that integrin
antagonists could protect RPE cells from detrimental effects induced by the interaction
with immune cells recruited to the retina. Overall, the leukocyte integrin antagonists
employed in the present study may represent a novel opportunity to develop new
drugs to fight dry AMD
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