883 research outputs found
Plastic number and possible optimal solutions for an Euclidean 2-matching in one dimension
In this work we consider the problem of finding the minimum-weight loop cover
of an undirected graph. This combinatorial optimization problem is called
2-matching and can be seen as a relaxation of the traveling salesman problem
since one does not have the unique loop condition. We consider this problem
both on the complete bipartite and complete graph embedded in a one dimensional
interval, the weights being chosen as a convex function of the Euclidean
distance between each couple of points. Randomness is introduced throwing
independently and uniformly the points in space. We derive the average optimal
cost in the limit of large number of points. We prove that the possible
solutions are characterized by the presence of "shoelace" loops containing 2 or
3 points of each type in the complete bipartite case, and 3, 4 or 5 points in
the complete one. This gives rise to an exponential number of possible
solutions scaling as p^N , where p is the plastic constant. This is at variance
to what happens in the previously studied one-dimensional models such as the
matching and the traveling salesman problem, where for every instance of the
disorder there is only one possible solution.Comment: 19 pages, 5 figure
Exact value for the average optimal cost of bipartite traveling-salesman and 2-factor problems in two dimensions
We show that the average cost for the traveling-salesman problem in two
dimensions, which is the archetypal problem in combinatorial optimization, in
the bipartite case, is simply related to the average cost of the assignment
problem with the same Euclidean, increasing, convex weights. In this way we
extend a result already known in one dimension where exact solutions are
avalaible. The recently determined average cost for the assignment when the
cost function is the square of the distance between the points provides
therefore an exact prediction for
large number of points . As a byproduct of our analysis also the loop
covering problem has the same optimal average cost. We also explain why this
result cannot be extended at higher dimensions. We numerically check the exact
predictions.Comment: 5 pages, 3 figure
Selberg integrals in 1D random Euclidean optimization problems
We consider a set of Euclidean optimization problems in one dimension, where
the cost function associated to the couple of points and is the
Euclidean distance between them to an arbitrary power , and the points
are chosen at random with flat measure. We derive the exact average cost for
the random assignment problem, for any number of points, by using Selberg's
integrals. Some variants of these integrals allows to derive also the exact
average cost for the bipartite travelling salesman problem.Comment: 9 pages, 2 figure
Large deviations of the free energy in the p-spin glass spherical model
We investigate the behavior of the rare fluctuations of the free energy in the p-spin spherical model, evaluating the corresponding rate function via the G\ue4rtner-Ellis theorem. This approach requires the knowledge of the analytic continuation of the disorder-averaged replicated partition function to arbitrary real number of replicas. In zero external magnetic field, we show via a one-step replica symmetry breaking calculation that the rate function is infinite for fluctuations of the free energy above its typical value, corresponding to an anomalous, superextensive suppression of rare fluctuations. We extend this calculation to nonzero magnetic field, showing that in this case this very large deviation disappears and we try to motivate this finding in light of a geometrical interpretation of the scaled cumulant generating function
Combined effects of electromagnetic fields on immune and nervous responses.
In technologically developed countries, there is concern about hazards from electromagnetic fields (EMFs). Several studies have reported that immune and neuroendocrine systems exert an integrated response to EMF exposure. The aim of this review is to summarize the results of studies on the effect of low and high frequency EMF on immune and neuroendocrine systems on which our research group has been working for several years
Asthma worsened by benzoate contained in some antiasthmatic drugs.
Here, we report our experience on benzoate hypersensitivity. Drug and food additives are known to induce pseudo-allergic reactions such as urticaria, eczema, asthma and rhinitis. These reactions are often under-diagnosed, above all in allergic patients treated with additive containing drugs. On the contrary, attention to additives present in some drug formulations and foods may often permit more correct diagnosis
Average optimal cost for the Euclidean TSP in one dimension
The traveling-salesman problem is one of the most studied combinatorial
optimization problems, because of the simplicity in its statement and the
difficulty in its solution. We study the traveling salesman problem when the
positions of the cities are chosen at random in the unit interval and the cost
associated to the travel between two cities is their distance elevated to an
arbitrary power . We characterize the optimal cycle and
compute the average optimal cost for every number of cities when the measure
used to choose the position of the cities is flat and asymptotically for large
number of cities in the other cases. We also show that the optimal cost is a
self-averaging quantity, and we test our analytical results with extensive
simulations.Comment: 14 pages, 8 figure
Immunopathogenesis of sarcoidosis and risk of malignancy: a lost truth?
The hypothesis of a relationship between sarcoidosis and malignancy was firstly formulated in 1972 by Brincker. He documented an association of sarcoid reactions or sarcoidosis with 19 lymphomas and associated malignancies. Based on various epidemiological studies, for more than 20 years sarcoidosis has been considered as a condition at increased risk for cancer, particularly lymphoproliferative disorders. The existence of a sarcoidosis-lymphoma syndrome was therefore proposed, highlighting, as a potential mechanism, the uncontrolled lymphocyte proliferation and mitotic activity. A reduced ability to eliminate an antigen and chronic inflammation have been suggested as triggering events. Leading to a reduced tumor immune surveillance, a diminished myeloid dendritic cells (mDC) function, despite up-regulated co-stimulatory and maturation markers, was also raised as potential mechanism. However, some subsequent studies have questioned the presence of a close association between the two entities and have explained those previously published as the result of selection bias and misclassification. Recently, a Swedish population-based cohort study documented a significant overall excess incidence of cancer among sarcoidosis patients, especially those with multiple hospitalizations or admission in older age, emphasizing again a potential neoplastic risk. Therefore, currently, whether these patients have an increased risk of developing malignant lesions is still debated. Larger and unbiased studies are needed before drawing definite conclusions
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