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Punctuated evolution of population genomics
No full textIn this thesis I apply population genetics methods and genotype-phenotype mapping to show that evolution has more discrete rather than linear pace and that this finding may reconcile between two evolution theories (punctuated equilibrium and phyletic gradualism
Constraining Modified Gravity Theories With Cosmology
No full textWe study and constrain the Hu and Sawicki f(R) model using CMB and weak
lensing forecasted data. We also use the same data to constrain extended theories of
gravity and the subclass of f(R) theories using a general parameterization describing
departures from General Relativity. Moreover we study and constrain also a Dark
Coupling model where Dark Energy and Dark Matter are coupled toghether
Biochemical, Virological and Epidemiological Aspects of HPV Genital Infection in Cervical Cancer Progression
No full text
ECOLOGY AND BEHAVIOUR OF THE EURASIAN OTTER (Lutra lutra) IN A MEDITERRANEAN AREA (ALENTEJO, PORTUGAL)
No full textDespite being a highly studied carnivore, the Eurasian otter (Lutra lutra) still offers the opportunity to explore many aspects of its ecology and behaviour that are poorly known or have only been investigated in temperate areas.
From April 2007 to October 2010, the OPA research project (Otter Project in Alentejo) was conducted in the south-central Alentejo region of Portugal, in an area of roughly 800 km2. Through the capture and subsequent radio-tracking of 16 wild Lutra lutra individuals (9 males and 7 females) for an average of 139 radio-locations per animal (about 126 days), together with the genotyping of 51 individual otters, the project aimed to provide a set of basic data on the biology and ecology of the species that were missing or limited throughout its extent of occurrence or in the Mediterranean environment. This thesis focus on some of the aspects of the referred project, such as: (1) extent of home ranges (HR) and movement patterns, including their relationships to seasonality and the availability (and its variability) of water resources; (2) genetic spatial structure, dispersal and social interactions; (3) activity rhythms; (4) habitat selection, with particular focus on the modality and frequency of use of reservoirs; (5) testing of a GPS GSM/GPRS telemetry system in riparian habitats and on free-ranging wild otters.
Concerning point (1), Network K-function analyses revealed a non-uniform use of home ranges in all monitored individuals of adult size, thus showing fidelity to their annual home range (site fidelity). On average, 49 radio-locations (fixes) (corresponding to approximately 45 days of tracking) were necessary to estimate a stable home range. The estimated average linear extension of home ranges was approximately 16.8 km for females (SE = 2.8) and 38.5 km for males (SE = 2.4), or 22.5 and 92.7 Ha respectively. The maximum extension recorded was 68.1 km (78.6 km including outliers). All individuals had at least one artificial reservoir within their home ranges, representing, on average, 32% of each home range.
Several measures of abundance and dispersion of water (which, in turn, also affect the dispersion of aquatic prey) were used in correlation analyses and multiple regression analyses, using Generalized Linear Models (GLM) with the extent of the monitored otters‟ home range as the response variable. The goal was to test the Resource Dispersion Hypothesis (RDH - Macdonald 1983), a hypothesis which predicts, amongst other, the extent of territories in terms of resource dispersion within them. All analyses conducted showed a general influence of abundance and dispersion on otters‟ home range size. However, the response of individuals to changes brought on by the arrival of summer drought was quite diverse. Besides sex and maturity of the animal, it was dependent on the characteristics of the main stream in which it lived and on its space use modality: animals that lived along waterways that have dried up less than the average showed smaller extents of HRs as well as those that consistently used one or a few lentic environments of limited size. Larger extents were usually associated with animals whose HRs were located in areas with high dispersion of water or with individuals which showed a less concentrated use of reservoirs. In general, it appears that the percentage of drought during the dry season determines the minimum HR size (when the otters would tend to enclose within their home ranges patches with a minimum amount of water), while during the wet season – when minimum size is already guaranteed – otters would expand their territories (home ranges) to the surrounding areas, increasing the possibilities of foraging and mating (area-minimizing strategy - Mitchell & Powell 2004, 2007).
During a single night (N = 54), otters used on average 3.7 km (SD = 2.9, range: 0 - 14.3) of the annual home range, moving 2 km (SD = 2.8, range: 0 - 22.9) away from the start point of activity (always coinciding with a known resting site) and covering a cumulative distance of 8.2 km (SD = 5.2, range: 0 - 24.2), with a revisiting index ranging from 0 to 4.23 (mean = 2.44, SD = 0.91). Between two fixes of a continuous monitoring session (documented every 15 minutes), the average displacement was 183 m (SD = 355, range 0 - 4271, N = 5609), at an average speed of 712 m/h (SD = 1308; range: 0 - 16325) (N = 5904).
All monitored otters (N = 19, including those tagged with GPS harnesses) showed high fidelity to the aquatic habitat, being always located (N = 10286) within a short distance from water (mean = 19 m, SD = 25, range: 0 - 521).
Most of the variability observed in movement parameters was caused by interactions between sex, age and season. In particular, adult males were the most mobile category and this was especially true during the wet season, when the greater abundance of water and the return of the hydric connectivity in the previously dried watercourses led to a larger extension in their movements and expansion of home ranges, probably in an attempt to maximize reproductive opportunities.
During the wet season movement parameters were generally higher in both sexes, while revisiting rates were higher in the dry season. Correlation analyses performed between movement patterns and variables concerning the dispersion and abundance of water showed that with an increase in the availability of watery sectors the otters increased the amplitude of their movements, reducing their visits to the same portions of their range; on the other side, with a greater fragmentation of the hydrography, indicated by a higher average percentage of dry sites, movements were less extensive and revisits more frequent. Such findings confirm the critical effect that the fragmentation in the availability of the water resource exerts on the biology and behaviour of otters in a Mediterranean environment.
Regarding point (2), a mixed approach consisting of genetic techniques and radio-telemetry was used with the following purposes: to verify the existence of a spatial structure in the relationship between individuals of the same population; to investigate the scale of the hypothetical relationship between degree of relatedness and geographic distance; to identify events of dispersal; to verify the hypothesis of a male-biased dispersal in this species; to study the social interactions between monitored individuals.
The molecular data refers to DNA extraction from 65 samples of tissue, hair, blood or fresh spraints collected during the project, which led to the genotyping of 51 individuals (28 females and 23 males).
These analyses revealed that spatially closer females (N = 286 paired combinations) were more related, while the same cannot be stated for males (N = 224 paired combinations). These patterns are suggestive of male-biased dispersal.
Surprisingly, the relationship between geographic distance and relatedness decreased after a threshold of about 30–40 km, suggesting the existence of isolation by distance between individuals of the study population at a fine spatial (and time) scale.
The first data on dispersal by this species obtained through radio tracking techniques are presented. These data are the first from a Mediterranean area and are an addition to the only previously reported case on this species (involving a one year old male of a Scottish population marked with radio-active zinc, which dispersed 68 km). Dispersal was detected only in males (N = 4), in a sample of 7 sub-adult individuals monitored; no events of dispersion were documented in either 2 sub-adult females (F6 and F8), nor in one of the males (M4), confirming evidences about male-biased dispersal gathered through molecular analyses. The dispersal distance was on average 20 km (SD = 6), ranging from 10 to 26 km (or 34 ± 9, range: 25 - 47, when expressed as cumulative distance traveled). Possible explanations of the short dispersal distances are discussed. Interestingly, of the 4 sub-adult males of which dispersal was detected, 3 followed the same route and ended up occupying (at different times) almost the same area, although they had potentially available different parts of river catchments and directions.
Still regarding the socio-spatial organization of the species, analyses of static and dynamic interactions were performed on individuals with neighbouring or overlapping home ranges. From these analyses, it appears that also in the Mediterranean study area the social organization of the species falls within the classical model of intrasexual territoriality typical of mustelids, with a polygynous breeding system. However, some discrepancies have emerged with regard to what is reported in literature. Contrary to the commonly referred solitary behaviour of the species, monitored otters showed a high degree of overlap in space and time (in some cases even sharing the same diurnal resting sites and even between a male and a female with cubs when the former was known for not being the father). By documenting a large portion of time spent together (not only during matings) by individuals of opposite sex, some flexibility in the social system of this species is highlighted.
The evidence gathered confirms the idea that the sociality of a species is complex and variable, and suggests the necessity to undertake further studies on the sociality of the Eurasian otter at the individual level and fine temporal and spatial scale in diverse areas.
The otters showed high levels of activity, with 45% of fixes documented as in activity and the remaining 55% at rest and the percentages rosing to 76 and 23, respectively, when considering only night fixes. The activity was, indeed, mainly nocturnal. Among the major determinants of circadian rhythms were foraging strategies (nocturnal hours are believed to present better conditions for catching the two major categories of prey: fish and red swamp crayfish), thermoregulation (to avoid extreme temperatures, both hot and cold), seasonal variability (higher activity during the wet season), age, dispersal events in young males and reproductive status in females. The onset of activity was correlated with sunset time, while the end of activity was less predictable. The hours of greatest activity were concentrated after sunset (from 21:00 to 22:00), in the middle of the night (from 2:00 to 3:00) and before dawn (around 5:00). Multiple regression analyses using generalized linear mixed-effect models (GLMM) showed a combined effect of several weather variables and micro-climatic conditions on nocturnal activity patterns. In particular, among other documented effects, extreme temperatures decrease the probability of finding an otter in activity. The same models, when applied to the width of movement undertaken by the otters, showed the influence of a smaller number of variables. It therefore seems that the decision to be active or not depends much on environmental descriptors, which may in turn regulate the activity rhythms of prey, while the choice to make a substantial move or not is mainly related to intrinsic factors such as sex, age and reproductive requirements. Such choice could also be conditioned by memory/cognitive maps related to resource location, territorial marking needs and interaction with conspecifics.
Habitat selection (point 4) was analyzed on a substantial sample of radio-monitored animals through a dual methodological approach, consisting in logistic regression in generalized linear mixed-effect models (GLMM) and the more traditional method of use/availability of Neu et al. (1974). The two methods were applied both on the whole set of fixes and only on the active ones.
The final model selected by the GLMM, regarding the probability of an otter visiting a specific sector (100 m) of its home range, seems to indicate that this is influenced by: the distance from the nearest known resting site (with probability decreasing the greater the distance); the type of habitat (water channels were less visited than dams, rivers and ponds), which is in turn dependent on the season (ponds are most visited during the dry season); the presence, during the dry season, of perennial pools; the distance from the site with the highest biomass of the red swamp crayfish (and, as a proxy, also of fish); the distance from the nearest dam (with probability decreasing the greater the distance); the distance from the nearest paved road (there is more chance of a site being visited the further away a road is); and the distance from home range boundaries (the farther from the boundaries, the less likely it is for an otter to visit a site).
The probability of otter activity in a particular section within its home range appeared to be influenced by the same factors. However, in this model: the distance from the nearest confluence was also selected (the farther from a confluence site, the lower the probability of selection by an otter during its period of activity); increased activity was associated in decreasing order with ponds, dams and rivers, while in the first model the order was dams, rivers and ponds (it is to be noted that these three habitat types are the most selected in both models). Furthermore, there is a different order in the importance of the variables‟ effects due to slight variations in the estimates of their coefficients and some minor differences in the estimates of the coefficients of the same variables, mainly regarding to the distance from the nearest resting site, which appears greater in the first than in the second model (as expected, since the first also includes fixes during the day, when the otters are on most occasions inactive in their resting sites).
All the analyses performed on habitat selection highlight a continuous use of lentic habitats by the otters throughout the year and not just during summer months as previously hypothesized in literature. Reservoirs appear to be selected in particular because of prey abundance (mainly fish, here, on average, more abundant), but, being scarce in terms of cover (therefore shelter availability), they are much less used for resting, for which otters selected streams in the majority of cases. These, however, are also used for foraging, especially for the red swamp crayfish, which is here, on average, more abundant. Ponds are used quite frequently for both activity and rest and they seem to play an important role during cubs‟ raising. The behaviour shown by monitored individuals is consistent with habitat selection already occurring at the landscape scale (second-order selection - Johnson 1980). The selection of streams (in primis) and ponds for resting seems to be due to the high availability of riparian vegetation. Results obtained here therefore highlight the need of a set of habitats for the otter in a Mediterranean context: lentic ones, which serve as main source of water and prey during the extreme summer drought, and lotic ones, richer in riparian vegetation and which therefore provide shelter and conditions for prey resilience in the intermittent isolated pools, confirming what was previously suggested by studies carried out by indirect methods (presence signs‟ surveys).
A low-cost GPS GSM-GPRS system (point 5), developed by the Dutch Otterstation Foundation (Netherlands), has been tested in this project for the first time on an otter species (through the use of harnesses). This tool allowed to track animals (N = 6, 711 locations, for a mean period of 9 days and the rate of acquisition of the GPS signal 68.2%) with a high frequency (otherwise impossible based only on man-powered field work) and resulted in a good accuracy level (average error = 8.9 m, SD = 8.5). This experiment was also the first test of a GPS technology in a riparian habitat and on a fresh-water diving animal.
The collection of dead animals enabled to expand the sample and to acquire some information on demographic parameters of the studied otter population as well as to perform some morphometric measurements.
In particular, the population had a sex ratio of 0.8 males per one female (N = 51), broken down into 39% cubs, 39% adults and 26% sub-adult individuals (N = 40). The estimated average age was 2.2 years (SD = 2.5), with a maximum of 11 years (one female specimen). Death by anthropic causes was noticeable, the major mortality factor being represented by road accidents (62%, N = 24). Mortality events were mainly distributed in the first two months of autumn, after the summer droughts.
From the morphometric measurements collected on a sample of 35 animals, the average weight of male individuals was 8.5 kg (SD = 0.9, N = 5) and that of females 6.6 kg (SD = 1.0, N = 10). Average body length was 123.6 cm (SD = 2.6) for males and 111.9 cm (DS = 3.5) for females.
Estimates of otter density within individual home ranges of 5 monitored females varied from 0.23 (± 0.05) alle 0.53 (± 0.16) otters per km, depending on whether they are referred to the entire portion of the used water network or only to main rivers respectively.
The number of otters captured (N = 47), in particular those equipped with intraperitoneal radio-transmitters (N = 16), together with the long-term average monitoring period per animal (401 days), were higher than those of previous studies of radio tracking of Lutra lutra. This allowed to identify a correct protocol of capture (including the testing of different trapping alarm systems), surgical implant and radio-monitoring of the species, as well as to extend the obtained inferences at a population level.
The mixed approach, consisting of radio tracking and molecular techniques, combined with the collection of a fair number of deceased animals in the study area, enabled to gain a wealth of information at the individual level and for a reasonable period of time (about 3 ½ years), covering different aspects of the ecology of a population.
The results here provided reveal previously unknown or little known aspects of the eco-ethology of the species, particularly in a Mediterranean environment, such as extents of home-ranges, habitat use and selection, movement and activity patterns, social interactions, dispersal, spatial structure of the relatedness between individuals and density of population. They therefore constitute a source of important information for proper management and conservation of this species in the Portuguese territory (and possibly applicable to other Mediterranean environments).
Although the conservation status of otters in Portugal is reassuring, all the evidence collected during this study emphasizes that the Mediterranean populations of this species are subject to significant risks associated with their dependence on water. Different evidence on how the ecology and behaviour of the species are strongly influenced by the climatic characteristics of the Mediterranean environment and the fragmentation and high variability in the availability of the water resource caused by droughts were indeed provided. Such evidence highlight that otters are potentially affected by climate change already in the present and in many aspects of their ecology/behaviour, confirming what was recently suggested for the future distribution of the species through climate simulation models (Cianfrani et al. 2011).external referees were: prof Anna Loy (Università del Molise - Italy) and prof Sandro Lovari (Università di Siena - Italy).the PhD project was basically funded by Lorenzo Quaglietta's fellowship, with a little help from Fundaçao Luis de Molina (Evora University - Portugal)
"CT EVALUATION OF CORTICAL BONE THICKNESS AND DENSITY FOR ORTHODONTIC MINI-IMPLANT PLACEMENT”
No full textIntroduction:
There is the evidence that cortical bone thickness(CBT) and cortical bone quality(CBQ) can have a strong impact on primary stability and overall success of mini-implants.
This study evaluated quantity(thickness) and quality(density) differences of cortical bone between interradicular sites to provide guidelines for mini-implant placement.
Material and method:
The maxilla or mandibula CT scans of 45 patients treated at the Department of Orthodontics of “Sapienza” University of Rome were selected. The selected patients were divided in two groups: adolescent group(aG)(range 12-18 years) and adult group(AG)(range19-50years). Using SimPlant software (Materialise, Leuven, Belgium),a program that allows reconstruction of 3D models and images of anatomical structures along planes and curves from data acquired with CT, the CBT and CBQ was measured at 2,4,6 and 8 mm intervals apical to the alveolar crest at each interradicular sites in both maxilla and mandible.
A cube of 1mm was used to measure the density of cortical bone at each level. The CBT values were described in millimeters(mm) and CBQ values in Hounsfield units (HU). Data was evaluated using a statistical analysis software (SPSS® software (Statistical Package for Social Science, IBM Corporation, NY-USA). Quantitative data of each group was described with mean values. Considering the values of thickness and density , the T-test was used to determine the influence of different gender , age and arch on CBT and CBQ values. The significance was set at P≤.05. Correlations between thickness , density and level of measurements were tested with the Pearson correlation coefficient. The significance was set at P≤.01.
Results:
Considering CBT in aG the average values ranged from 1.19mm to 1.83mm; in AG the average values ranged from 1.25mm to 1.99mm.
Considering CBQ in aG the average values ranged from 910.03HU to 1461.61HU; in AG the average values ranged from 777.43HU to 1327.90HU.
The mandibular CBT was higher both on the vestibular(P≤.000)and lingual/palatal side(P≤.013).
The mandibular CBQ was higher both on the vestibular(P≤.000)and lingual/palatal side(P≤.027).
In the male CBT and CQB were higher than female both on the vestibular and lingual/palatal side with in each case an equal significance value(P≤.000).
Comparing , finally, the CBT and CBQ values of aG and AG , the aG showed a higher thickness and bone density but the data was statistically significant only comparing the lingual/palatal CBT(P≤.001).
Conclusion:
The results of the present study demonstrated an higher CBT and CBQ values in the mandibular interradicular sites of adolescent males.Prof.michile cassetta
LO SLUM UPGRADING, GLI OBIETTIVI DEL MILLENNIO E LA PIANIFICAZIONE STRATEGICA PARTECIPATA PER LO SVILUPPO: IL CASO AFRICANO
No full textStudi analitici e farmacologici sulla 25-idrossivitamina D
No full textLa carenza di vitamina D è una condizione molto diffusa nella popolazione generale in diverse aree geografiche, anche se tale fenomeno è generalmente sottovalutato. Numerose evidenze sperimentali e cliniche dimostrano come la carenza di vitamina D rappresenti non soltanto un importante fattore condizionante la salute scheletrica, ma anche una possibile concausa nella patogenesi di numerose malattie croniche. La corretta determinazione dello stato vitaminico D, espresso in termini di concentrazione sierica di 25-idrossivitamina D (25OHD), rappresenta pertanto una problematica ancora aperta.
I metodi comunemente utilizzati per la determinazione della 25OHD, pur essendo provvisti di adeguata sensibilità, presentano tuttavia diversi svantaggi, tra i quali, in particolare: lo smaltimento del materiale radioattivo richiesto per l’analisi, il pretrattamento dei campioni, il costo della strumentazione e l’impiego di personale tecnico specializzato. Tali caratteristiche si traducono in un costo generalmente elevato delle analisi.
Questa tesi di dottorato si è articolata attraverso uno studio sia analitico che farmacologico sulla 25OHD.
In particolare, lo studio analitico ha riguardato lo sviluppo di un nuovo metodo di determinazione
della 25OHD basato sull’impiego di sensori ottici ed elettrochimici, allo scopo di valutarne il possibile impiego nella pratica clinica. Abbiamo pertanto inizialmente sviluppato un metodo per la determinazione diretta della 25OHD attraverso una reazione antigene-anticorpo, utilizzando un immunosensore di tipo ottico che impiega la risonanza plasmonica superficiale (SPR) come elemento di trasduzione. Impiegando questo dispositivo è stato ottenuto un limite di rivelabilità (LOD) di ca. 2 µg/ml, che tuttavia rappresenta un valore troppo elevato per consentirne l’impiego nella pratica clinica. Allo scopo di aumentare la sensibilità, la 25OHD è stata modificata con una nanoparticella d’oro (AuNPs): ciò ha permesso di raddoppiare la sensibilità e di ridurre il LOD a ca. 1 µg/ml. L’impossibilità di determinare la 25OHD mediante l’impiego di anticorpi, sia direttamente che tramite funzionalizzazione, ha spostato la ricerca verso una determinazione indiretta mediante l’impiego della Vitamin D Binding Protein (VDBP): in questo caso la 25OHD è stata immobilizzata sulla superficie del sensore SPR utilizzando la molecola O-(2-aminoetil)-O′-(2-maleimidoetil) etilene glicol trifluoroacetato (AMEG) che reagisce con la vitamina D attraverso una reazione di Diels-Alder. Quindi la 25OHD è stata determinata mediante un saggio di tipo competitivo che ha abbassato il LOD a ca. 45 ng/ml che apre concrete e interessanti prospettive per l’utilizzo di questa metodica su matrici reali.
Al fine di poter realizzare dispositivi per analisi portatili, è stato ideato un immunosensore
elettrochimico utilizzando come trasduttori elettrodi d’oro realizzati mediante stampa serigrafica (Screen Printed Electrodes, SPE). Non avendo la 25OHD natura chimica elettroattiva è stato necessario funzionalizzare la 25OHD con una molecola opportuna: a tale scopo è stato utilizzzato il
4-ferrocenilmetil-1,2,4-triazolin-3,5-dione (FMTAD), molecola che lega la 25OHD attraverso una reazione di Diels-Alder, rendendo possibile l’analisi voltammetrica della 25OHD grazie alle proprietà elettroattive della sua funzione ferrocenilica, portando il LOD a 10 ng/ml, ovvero un valore che può considerarsi adeguato per l’applicazione di questa metodica alla determinazione della vitamina D in campioni reali.
Scopo dello studio di intervento è stato di valutare gli effetti della somministrazione ripetuta di calcidiolo (25OHD3) sui principali parametri biochimici del metabolismo scheletrico in 18 soggetti normali di sesso femminile. Abbiamo pertanto somministrato una singola dose di 500 microgrammi al mese di calcidiolo, per 4 mesi consecutivi, al fine di valutarne il possibile utilizzo in alternativa alla somministrazione del colecalciferolo (vitamina D3) nella pratica clinica. Tale impiego infatti potrebbe rappresentare un vantaggio soprattutto in quei soggetti nei quali, in presenza di particolari condizioni cliniche, la somministrazione della vitamina D potrebbe non essere il migliore intervento terapeutico
IL POTERE DISCIPLINARE TRA DETTATO NORMATIVO, ESPERIENZA GIURISPRUDENZIALE E RUOLO DELL'AUTONOMIA COLLETTIVA
No full textNel primo capitolo, intitolato “La giurisprudenza in materia di esercizio del potere disciplinare”, si è inteso ricostruisce il percorso intrapreso dalla giurisprudenza di legittimità, analizzato in parallelo con quello dottrinale, al fine di individuare la fonte normativa del potere disciplinare nel contratto individuale di lavoro e di definire l’ambito soggettivo ed oggettivo di applicazione delle garanzie procedimentali poste dall’art. 7 dello Statuto dei Lavoratori. Nel secondo capitolo, dedicato a “Il sistema di garanzie ed il ruolo dell’autonomia collettiva”, si è analizzato l’intervento operato dai principali ccnl di categoria in materia disciplinare approfondendone l’interpretazione giurisprudenziale. E’ stata, inoltre, posta l’attenzione sul processo di delegificazione avviato con l’art. 8 della legge 148/2011 individuandone le possibili deroghe all’art. 7 dello Statuto dei lavoratori ed alla rogolamentazione pattizia sopra citata.
E’ stata, altresì, sottolineata l’opposta tendenza di rilefigicazione avvenuta nell’ambito del pubblico impiego contrattualizzato ad opera del d. lgs. 150/2009 (c.d. riforma Brunetta).
Nel terzo, ed ultimo capitolo, riservato a “L’esercizio del potere disciplinare nel settore autoferrotranvieri”, si è indagato nell’ambito della regolamentazione speciale cui soggiace il rapporto di lavoro della categoria analizzandone la norma di riferimento, il Regolamento All. A) al R.D. 148/1931
The Stable Set Problem: Some Structural Properties and Relaxations
No full textGiven a graph, the edge formulation of the stable set problem is defined by two-variable constraints, one for each edge, expressing the simple condition that two adjacent nodes cannot belong to a stable set. We study the fractional stable set polytope, i.e. the polytope defined by the linear relaxation of the edge formulation. Even if this polytope is a weak approximation of the stable set polytope, its simple geometrical structure provides deep theoretical insight as well as interesting algorithmic opportunities.
Exploiting a graphic characterization of the bases, we first redefine simplex pivots in terms of simple graphic operations, that turn a given basis into an adjacent one. Between all possible pivots, we characterize degenerate and non-degenerate ones, and we differentiate those leading to an integer or to a fractional vertex. The graphic characterization of bases is crucial to prove another structural property of the fractional stable set polytope, concerning the adjacency of its vertices. In particular, we extend a necessary and sufficient condition due to Chvátal for adjacency of (integer) vertices of the stable set polytope to arbitrary (and possibly fractional) vertices of the fractional stable set polytope. These results lead us to prove that the Hirsch Conjecture is true for the fractional stable set polytope, i.e. the combinatorial diameter of this fractional polytope is at most equal to the number of edges of the given graph. We actually refine this bound in the non-bipartite case by proving a tighter bound, equal to the number of nodes of the graph. We also design a simplex-like algorithm for the stable set problem that relies on the adjacency properties mentioned above. Our algorithm generates only integer solutions without using cutting plane methods. Preliminary results are encouraging but show that cycling can occur, due to the high degree of degeneracy of the polytope. Nevertheless, the perspective of an exact combinatorial method of solution for the stable set problem based on this algorithm seems intriguing, provided that an anti-cycling rule is embedded in its current design.
The graphic characterization of bases also provides a significant assessment on strength of different corner relaxations for the edge formulation of the Maximum Cardinality Stable Set Problem.
The corner relaxation of a mixed-integer linear program is a central concept in cutting plane theory. In a recent paper Fischetti and Monaci provide an empirical study of the strength of the corner and other related relaxations on benchmark problems. We validate with theoretical arguments the empirical results obtained by Fischetti and Monaci: we give a precise characterization of the bounds given by the corner relaxation and three of its extensions in the special case of the edge formulation of the stable set problem, for which a full description of the corner polyhedron is available. Our theoretical analysis shows that degeneracy plays a major role, as the difference in the bounds given by corner relaxations from two different optimal bases can be significantly large. Therefore, exploiting multiple degenerate bases for cut generation could give better bounds than working with just a single basis.
Finally, a concave reformulation for Set Covering problems is presented, where integrality constraints are dropped and the original linear objective function is replaced by a concave one, penalizing fractional values. For such reformulation, any integer local optimum corresponds to a heuristic solution of the original problem. To determine local optima of our concave reformulation, we apply the Frank-Wolfe algorithm with a multi-start approach. The choice of a suitable parametric concave function allows us to regulate the smoothness of the objective function and to achieve sparseness of the local optimum. When applied to the edge formulation of the stable set problem, additional properties of local optima can be established. Namely, if the parameter of the objective function belongs to a certain range, binary valued variables of the local optimum can be fixed, allowing a reduction of the dimension of the problem. Computational experiments show that the concave heuristic is effective on some difficult benchmark problems