On d-graceful labelings

In this paper we introduce a generalization of the well known concept of a graceful labeling. Given a graph G with e=dm edges, we call d-graceful labeling of G an injective function from V(G) to the set {0,1,2,..., d(m+1)-1} such that {|f(x)-f(y)| | [x,y]\in E(G)} ={1,2,3,...,d(m+1)-1}-{m+1,2(m+1),...,(d-1)(m+1)}. In the case of d=1 and of d=e we find the classical notion of a graceful labeling and of an odd graceful labeling, respectively. Also, we call d-graceful \alpha-labeling of a bipartite graph G a d-graceful labeling of G with the property that its maximum value on one of the two bipartite sets does not reach its minimum value on the other one. We show that these new concepts allow to obtain certain cyclic graph decompositions. We investigate the existence of d-graceful \alpha-labelings for several classes of bipartite graphs, completely solving the problem for paths and stars and giving partial results about cycles of even length and ladders.Comment: In press on Ars Combi

A generalization of the problem of Mariusz Meszka

Mariusz Meszka has conjectured that given a prime p=2n+1 and a list L containing n positive integers not exceeding n there exists a near 1-factor in K_p whose list of edge-lengths is L. In this paper we propose a generalization of this problem to the case in which p is an odd integer not necessarily prime. In particular, we give a necessary condition for the existence of such a near 1-factor for any odd integer p. We show that this condition is also sufficient for any list L whose underlying set S has size 1, 2, or n. Then we prove that the conjecture is true if S={1,2,t} for any positive integer t not coprime with the order p of the complete graph. Also, we give partial results when t and p are coprime. Finally, we present a complete solution for t<12.Comment: 15 page

Corporate Governance, Corporate and Employment Law, and the Costs of Expropriation

We set up a model to study how ownership structure, corporate law and employment law interact to set the incentives that infl uence the decision by the large shareholder or manager effectively controlling the fi rm to divert resources from minority shareholders and employees. We suggest that agency problems between the controller and other investors and holdup problems between shareholders and employees are connected if the controller bears private costs of “expropriating” these groups. Corporate law and employment law may therefore somethimes be substitutes; employees may benefi t from better corporate law intended to protect minority shareholder, and vice versa. Our model has implications for the domestic and comparative study of corporate governance structure and addresses, among other things, the question whether large shareholders are better able to “bond” with employees than dispersed ones, or whether the separation of ownership facilitates longterm relationships with labor

Corporate Governance, Corporate and Employment Law, and the Costs of Expropriation

We set up a model to study how ownership structure, corporate law and employment law interact to set the incentives that influence the decision by the large shareholder or manager effectively controlling the firm to divert resources from minority shareholders and employees. We suggest that agency problems between the controller and other investors and holdup problems between shareholders and employees are connected if the controller bears private costs of “expropriating” these groups. Corporate law and employment law may therefore somethimes be substitutes; employees may benefit from better corporate law intended to protect minority shareholder, and viceversa. Our model has implications for the domestic and comparative study of corporate governance structure and addresses, among other things, the question whether large shareholders are better able to “bond” with employees than dispersed ones, or whether the separation of ownership facilitates longterm relationships with labor.

Algunos rasgos morfológicos de la llanura cordobesa entre la dislocación de San José del Salteño y el meridiano 62º 45' W*

Fil: Pasotti, Pierina. Universidad Nacional de Cuyo. Facultad de Filosofía y Letra

A problem on partial sums in abelian groups

In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we present some results about the validity of these conjectures

Globally simple Heffter arrays and orthogonal cyclic cycle decompositions

In this paper we introduce a particular class of Heffter arrays, called globally simple Heffter arrays, whose existence gives at once orthogonal cyclic cycle decompositions of the complete graph and of the cocktail party graph. In particular we provide explicit constructions of such decompositions for cycles of length $k\leq 10$. Furthermore, starting from our Heffter arrays we also obtain biembeddings of two $k$-cycle decompositions on orientable surfaces.Comment: The present version also considers the problem of biembedding

Impact of climate-induced dynamics on a coastal benthic ecosystem from the West Antarctic Peninsula

Climate change is globally recognized to pose a serious threat to sustainable human development and to the future of our planet. Both the palaeoclimate and the recent global warming have exhibited larger magnitude of effects on both polar regions (the so-called polar amplification), with some areas showing increases in mean air temperatures double that of the global average at both poles. In the Antarctic there is a strong regional pattern in the effects of climate change. The West Antarctic Peninsula (WAP) region, the area hosting the highest biodiversity of the whole Antarctic continent, is one of the fastest warming (and changing) regions of the planet, whereas the continental Antarctic presents a general cooling trend. In the WAP air temperatures have increased in both summer and winter (1950-2001: summer + 2.4 ± 1.7°C century-1, autumn +6.2 ± 6.0°C century-1), the sea ice (land fastened ice – or fast ice – versus drift and “pack” ice) ‘season’ and extent have dramatically reduced and more than 87% of the WAP glaciers have actively retreated in the past decades. The increases in glacier retreat observed since as early as the 1930-1950s are coupled to intense summer glacial discharge (e.g. via glacial melt waters), snow and permafrost melting and related effects on coastal sea water turbidity and salinity. Moreover, the decrease in fast ice season has led to higher frequency of iceberg scouring, the major driver of Antarctic shelf biodiversity. All these processes affect the marine coastal communities with direct and indirect effects. The increase in intensity of the observed changes in the WAP appears to fall yet among the natural variability of the past 380-2000 years of climatic history of the region, but anthropogenic drivers are foreseen to become more important in the whole continent by the end of 21st century. Therefore, the understanding of biological responses to the WAP the recent environmental change context represents a fundamental baseline for the deepening of our knowledge on benthic assemblages ecology and their resilience to likely future changes. In this study we investigated the benthic assemblage of Potter Cove (PC), a fjord-like embayment located on the southern coast of King George Island (KGI, South Shetland Islands, WAP). The cove is experiencing strong environmental changes and rapid glacier retreat has influenced the cove since the 1950’s. Potter Cove benthic assemblages are shaped by the interaction of iceberg scour, which can affect the benthos down to 20 m depth, sediment-laden melt water discharge and wave action. Recently community shifts have been reported in the cove for macroepibenthic assemblages. With the present study we focused on the shallow soft-bottom meio- and macrobenthos, and we deepened our investigation by looking at the important microbiota (prokariotes and microphytobenthos) assemblage, which is involved in the basal biogeochemical processes that model and characterize the sediment environment in which these metazoans live. In a spatial analysis we identified three contrasting sites (with different glacier retreat-related history), and investigated three size classes of organisms (microbiota, meio- and macrofauna) and interpreted their assemblage structure in light of their different turnover rates, feeding strategies and dispersal potential, making inferences on the historical influences of the glacier retreat on the resident benthic communities and detecting possible size-related biological responses. With a temporal analysis of the in situ meiofauna standing stocks we looked at possible effects of seasonality on the main meiofauna organisms. Moreover we contributed to the interpretation of these results by means of laboratory experiments to unravel potential effects of distinct glacial-related environmental stressors on PC meiobenthos (see Fig. 1). In the first study (Chapter II) we investigated three size classes of benthic biota (microbenthos, meiofauna and macrofauna) at three shallow water stations (each at a depth of 15 m) in the inner cove, which are influenced by different glacial, meltwater, and water current conditions. Isla D (62° 13' 32.6" S, 58° 38' 32" W) is the most recently ice-free area, being exposed since 2003, and situated about 200-215 m away from the glacier front. Faro station (62° 13' 32.6" S, 58° 40' 03.7"W) is situated on the northern side of the cove and became ice-free between 1988 and 1995. It is an area that is characterized by low ice disturbance and it is affected by wave action. The third station, “Creek” station was located adjacent to “Potter Creek” (62° 13‘ 57.3" S, 58° 39’ 25.9" W). This location has been ice-free since the early 1950s and is influenced by a meltwater river that forms during summer. It is also an area where the impact of growler ice, which can scour the benthos in PC up to a depth of 20 m (Kowalke and Abele, 1998; Sahade et al., 1998b). Such a study across different size spectra of the benthos is unique for the Antarctic shallow water marine environment. Our results revealed the presence of a patchy distribution of highly divergent benthic assemblages within a relatively small area (about 1 km2). In areas with frequent ice scouring and higher sediment accumulation rates, an assemblage mainly dominated by macrobenthic scavengers (such as the polychaete Barrukia cristata), vagile organisms, and younger individuals of sessile species (such as the bivalve Yoldia eightsi) was found. Macrofauna were low in abundance and very patchily distributed in recently ice-free areas close to the glacier, whereas the pioneer nematode genus Microlaimus reached a higher relative abundance in these newly exposed sites. The most diverse and abundant macrofaunal assemblage was found in areas most remote from recent glacier influence. By contrast the meiofauna showed relatively low densities in these areas. The three benthic size classes appeared to respond in different ways to disturbances likely related to ice retreat, suggesting that the capacity to adapt and colonize habitats is dependent on both body size and specific life traits. Chapter III was a continuation of the first investigation where we focused on the trophic interactions happening at these contrasting locations. We compared the meio- and macrofauna isotopic niche widths (δ13C and δ15N stable isotope analysis) by means of new generation Bayesian-based statistical approaches. The isotopic niches appeared to be locally shaped by the different degrees of glacier retreat-related disturbance observed within the cove. The retreat of the glacier seems to favor wider isotopic niches lowering initial local competition. The retreat of the ice is known to provide for new available resource pools via macroalgae colonization and likely punctual enhanced sea ice algae sedimentation. An intermediate-high and continuous state of glacial disturbance (e.g. ice-growlers) allows new species and new life strategies to settle during repeated colonization processes. The smaller benthic organisms (e.g. meiofauna) seemed to be the primary colonizers of these disturbed sediments, showing a wider isotopic niche. Ice-scour and glacial impact hence can play a two-fold role within the cove: i) they either stimulate trophic diversity by allowing continuous re-colonizations of meiobenthic species or, ii) in time, they may force the benthic assemblages into a more compacted trophic structure with increased level of connectedness and resource recycling. To conclude the in field work, in Chapter IV we investigated the seasonal responses of the meiobenthic assemblage at two shallow sites, located on the opposite shores of the inner Potter Cove (North Barton Peninsula versus South Potter Peninsula). We focused on responses to summer/winter biogeochemical conditions. Meiofaunal densities were found to be higher in summer and lower in winter, although this result was not significantly related to the in situ availability of organic matter in each season. The combination of food quality and competition for food amongst higher trophic levels may have played a role in determining the standing stocks at the two sites. Meiobenthic winter abundances were sufficiently high (always above 1000 individuals per 10 cm2) to infer that energy sources were not limiting during winter, supporting observations from other studies for both shallow water and continental shelf Antarctic ecosystems. Recruitment within meiofaunal communities was coupled to the local seasonal dynamics for harpacticoid copepods but not for nematodes, suggesting that species-specific life history or trophic features form an important element of the responses observed. The experimental part of the thesis starts with a tracer experiment (Chapter V). Antarctic meiofauna trophic position in the food web is to date still poorly studied. Primary producers, such as phytoplankton, and bacteria may represent important food sources for shallow water metazoans and the role of meiobenthos in the benthic-pelagic coupling represents an important brick for food web understanding. In a laboratory feeding experiment 13C-labelled freeze-dried diatoms (Thalassiosira weissflogii) and bacteria were added to retrieved cores from Potter Cove (15 m depth, November 2007) in order to investigate the uptake by 3 main meiofauna taxa: nematodes, copepods and cumaceans. In the surface sediment layers nematodes showed no real difference in uptake of both food sources. This outcome was supported by the natural δ13C values and the community genus composition. In the first centimeter layer, the dominant genus was Daptonema which is known to be opportunistic, feeding on both bacteria and diatoms. Copepods and cumaceans on the other hand appeared to feed more on diatoms than on bacteria. This may point at a better adaptation to input of primary production from the water column. On the other hand, the overall carbon uptake of the given food sources was quite low for all taxa, indicating that likely other food sources might be of relevance for these meiobenthic organisms. Chapter VI deals with the possible effects of climate change-related increases in inorganic sedimentation, mechanical disturbance and changes in food quality by means of two laboratory experiments: i) the effect of inorganic sedimentation (SED) on the vertical distribution of the meiofauna and ii) the effects of sediment displacement and different types of food (SEL) on the composition of meiobenthic and nematode assemblages in surface sediments. In the SED experiment there was no effect of the sediment load and variances in the densities were too high to allow any deeper understanding. In the SEL experiment the mechanical disturbance mimicked during the collection of the natural sediment caused significant losses in the densities of nauplii and copepods, which may have escaped or showed to be sensitive to this type of disturbance. Among the nematode assemblage, Aponema had an overall increase in relative abundance in the experimental units, benefiting of the sediment mechanical re-working. The different kind of detritus given in the microcosm (shredded macroalgae, the benthic diatom Seminavis robusta and the haptophyte Isochrysis galbana) did not result in significant differences among treatments in terms of meiofaunacomposition at higher taxon level. The nematode assemblage however, was dominated by epistrate feeders in the control and the S. robusta treatments resembling the natural background nematode assemblage. The macroalgae and the haptophyte detritus seemed to stimulate the presence of non-selective deposit feeders. The genus Sabatieria reached the highest relative abundance in these samples compared to both the other treatment and the background sediments, possibly because of increased hypoxic conditions in the presence of this type of detritus. Unfortunately, the high variances found in the experimental units hindered the finding of unequivocal effects on the nematode assemblages in both experiments. The data obtained in the current study indicates that Potter Cove’s shallow benthos is responding to in situ glacial retreat with structural (biomass and taxonomic composition) and functional (isotopic niche width) changes and that meiofaunal organisms appear to be the most resilient size class. Glacier retreat-related impacts on biological communities, hence, depend on the affected organisms turnover (recruitment potential), dispersal potential (capacity of re-colonisation or local migration), motility (avoidance of ice scour impact) and dietary flexibility (resilience to overall disturbances). The meiofauna, being connected to both the detritus and microorganisms on the one hand and the macrofauna on the other, displays a higher resilience to disturbance in light of an intrinsic size-dependent centrality in the overall benthic food web and the high trophic redundancy found between species of important taxons (e.g. nematodes). Inorganic sedimentation per se does not affect meiofauna abundances. Nematodes and copepods seem resilient to this disturbance. Fresh phytoplanktonic detritus may have positive effects on their abundance. Food quality changes (increase in macroalgae detritus and more accessible soft-celled phytoplankton flagellates) can stimulate bacterial degradation within the sediment and initiate short-term community shifts in the nematofauna with genera like Sabatieria or Halalaimus becoming more abundant. Abundances can be temporally negatively affected, especially those of oxygen sensitive taxa (e.g. harpacticoid copepods). Ice scour seems to have a negative effect on nematode selective feeders relative abundance. Ice scour and wind-driven re-suspension are very important disturbances with both “positive” and “negative” effects on the benthos, with wind affecting depths of up to 30 m during strong storms events. Iceberg scouring is the main driver of biodiversity in the Antarctic shelf since it increases the spatial heterogeneity and allow more species with different life strategies to co-exist in rather restricted areas. Anyhow, increases in their frequency are likely to become detrimental to most macrobenthic species, with overall strong influences, but not catastrophic consequences, for the highly detritus based meiobenthic assemblage. Meiofauna represents a pioneer size-class for newly ice-free, heavily scoured soft-bottoms, where wind-driven re-suspension is lower. Macrofauna is a poorer competitor at high disturbances but increases its dominance at intermediate-low disturbance levels. In the second situation competition for resources between meiofauna and macrofauna may become more important in shaping their relative community structure and the food web. Future scenarios in Antarctic marine ecosystems such as PC foresee a more or less rapid stop in iceberg scouring due to a complete withdraw of the glacier on land and a gradual decrease in melt water discharge parallel to KGI ice mass loss generated by the increasing temperatures. Therefore in the future wind speed-related wave action might be the only structuring force enacting on PC benthic communities, but to date there are no evidences of its direct effects on these organisms. In light of the important structuring effect of iceberg scouring and the highly hierarchical competition of Antarctic benthic assemblages, in the absence of this forcing, we might expect, on the longer term, a general decrease in macrobenthic resilience (both resistance to changes and recovery after disturbance), but a rather unchanged (although fluctuating on the short term) resilience for the meiobenthic assemblage