New Algorithms for Solving Tropical Linear Systems

The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is known, although counterexamples for existing pseudopolynomial algorithms are (and have to be) very complex. In this work, we continue the study of algorithms for solving tropical linear systems. First, we present a new reformulation of Grigoriev's algorithm that brings it closer to the algorithm of Akian, Gaubert, and Guterman; this lets us formulate a whole family of new algorithms, and we present algorithms from this family for which no known superpolynomial counterexamples work. Second, we present a family of algorithms for solving overdetermined tropical systems. We show that for weakly overdetermined systems, there are polynomial algorithms in this family. We also present a concrete algorithm from this family that can solve a tropical linear system defined by an $m\times n$ matrix with maximal element $M$ in time $\Theta\left({m \choose n} \mathrm{poly}\left(m, n, \log M\right)\right)$, and this time matches the complexity of the best of previously known algorithms for feasibility testing.Comment: 17 page

The Past ‘Interpreter’. Historical Stratifications in the Ritual Symbolism of Saint Joseph Festivals and Holy Week in Sicily

I temi della continuità culturale e della "sopravvivenza" del simbolismo rituale sono stati al centro dibattito in campo religioso antropologico e storico. Sono diventati di nuovo di attualità in relazione alla la patrimonializzazione di feste religiose "tradizionali" come San Giuseppe e la Settimana Santa, festival il cui simbolismo rituale (banchetto sacro, processione, rami sempreverdi, pane rituale, canti e danze) mostra un'evidente radice pre-cristiana e agraria. Una serie di domande emergono sia sul l'utilità delle fonti storiche (archeologiche e documentarie) per quanto riguarda la comprensione delle realtà rituale temporanea, e sulla questione della continuità cronologica delle pratiche e delle credenze; Questi meritano di essere riconsiderate sulla base di nuove ricerche e osservazioni, considerando lo scioglimento di quella che è stata definita "civiltà rurale" e dei rinnovati interessi verso il patrimonio immateriale comunità alla ricerca delle loro matrici di identità. Possiamo e dobbiamo tornare a chiederci: può i token deterreni e immateriali del passato, anche i più remoti, ci aiutano a capire ciò che osserviamo contesti festivi in corso?The themes of cultural continuity and ‘survival’ of ritual symbolism have been at the centre of debate in the anthropological and historical religious fields. They became topical again in relation to the issue of the patrimonialization of ‘traditional’ religious festivals such as Saint Joseph and Holy Week, festivals whose ritual symbolism (sacred banquet, procession, evergreen branches, ritual breads, songs and dances) shows an evident pre-Christian and agrarian root. A number of questions emerge about both the usefulness of historical sources (archaeological and documentary) with regard to the understanding of contemporary ritual reality, and about the issue of the chronological continuity of practices and beliefs; these deserve to be reconsidered on the basis of renewed research and observations, considering the dissolution of what has been defined as ‘rural civilization’ and the renewed interests towards immaterial patrimony by communities searching for their identity matrices. We can and must go back to asking ourselves: can material and immaterial tokens of the past, even the remotest ones, help us understand what we observe in current festive contexts

The Welfare State, Redistribution and the Economy, Reciprocal Altruism, Consumer Rivalry and Second Best

Democratic countries with substantial inequality and where people believe that success depends on connections and luck induce political support for high tax rates and generous welfare states. Traditional wisdom is that such policies harm the economy, but there is not much evidence that countries with a large welfare state and substantial redistribution have worse economic performance and welfare. One important reason is that governments have been careful to invoke the principles of reciprocity and mutual obligations in the design of the welfare state. Unemployment benefits conditioned on work experience, no misconduct and search effort harm the economy less. Indeed, conditional benefits may even boost employment in an economy with efficiency wages. A second reason is that people care about relative incomes and become unhappy if others earn and consume much more than they do. This explains why people do not seem to get happier, even though societies grow richer and richer. With such consumer rivalry the government wishes to correct for the rat race, even if there is no need for redistribution, by taxing labour. A third reason is that in modern economies many distortions are present and removing one at a time may worsen economic performance. Conversely, increasing tax progression in economies with non-competitive labour markets induces wage moderation and boosts employment. A final reason is that countries with large welfare states typically introduce various progrowth policies as well.mutual obligations, altruism, relative incomes, happiness, redistributive taxation, demand management, second best, design of welfare state

New Waves, New Spaces: Estonian Experimental Cinema of the 1970s

Using the label of “new wave” in the context of Estonian cinema is highly problematic and controversial because, unlike in France or, to take a more similar socio-political framework, in Czechoslovakia, the (Soviet) Estonian filmic arena did not see a creative outburst synchronous with and comparable to, both in scope of innovative production and international acclaim, the cinematic practices adorned with the adjective “new” elsewhere in Europe. While the heyday of various new waves, both in Western Europe and in the Soviet bloc, is normally limited to the period between the mid-1950s and the ruptures of 1968, in Estonia, as the local literary critic Mart Velsker (1999: 1211) has accurately argued, the essence of the innovative 1960s “is manifested in its most vivid form some time between 1968 and 1972, that is, at the end of the decade and partly even beyond it.” Compared to other artistic genres, however, Estonian cinema was severely lagging behind, both in achievement and in reputation. The true “Estonian New Wave” has been defined by local critics as born and burgeoning in the end of the 1970s and the beginning of the 1980s (Orav 2003: 54ff; Kärk 1995: 117; Kirt 1980: 33-4), when a new generation of young filmmakers entered the stagnated cinematic stage with bravado, finally inverting the low ebb that had lasted nearly a decade. Yet, in the midst of the ebbing waters of the early 1970s, a dark horse emerged, whose artistic contribution to Estonian cinematic heritage deserves to be identified as a new wave in miniature, a veritable diamond, albeit perhaps rough-cut. This author was Jaan Tooming, an actor and a theatre director, whose films constitute a fundamentally unprecedented phenomenon in Estonian cinema. His controversial, stylistically and semantically rich output, composed of unceasingly intriguing visual utterances, provides a fascinating order of spatial representations, which reconfigure Estonian cinematic territories in several respects and, at the same time, re-evaluate and criticize quite provocatively the historical and conceptual framework of imagining national, social and personal identities. The following investigation of Tooming’s films will concentrate chiefly on the spatial representations and practices, with digressions into the domain of re/constructing identities, both personal and collective