2,019 research outputs found
Fluctuations in the random-link matching problem
Using the replica approach and the cavity method, we study the fluctuations
of the optimal cost in the random-link matching problem. By means of replica
arguments, we derive the exact expression of its variance. Moreover, we study
the large deviation function, deriving its expression in two different ways,
namely using both the replica method and the cavity method.Comment: 9 pages, 3 figure
Two-Loop Corrections to Large Order Behavior of Theory
We consider the large order behavior of the perturbative expansion of the
scalar field theory in terms of a perturbative expansion around an
instanton solution. We have computed the series of the free energy up to
two-loop order in two and three dimension. Topologically there is only an
additional Feynman diagram with respect to the previously known one dimensional
case, but a careful treatment of renormalization is needed. The propagator and
Feynman diagrams were expressed in a form suitable for numerical evaluation. We
then obtained explicit expressions summing over distinct eigenvalues
determined numerically with the corresponding eigenfunctions.Comment: 12 pages, 2 figure
Investigation of refractory composites for liquid rocket engines Final report, 1 Oct. 1969 - 31 Oct. 1970
Oxidation resistance and high temperature tests of rhenium, tungsten, hafnium, and tantalum matrix composites with iridium in oxygen, fluorine, and boron atmospheres for liquid propellant engine
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
High-dimensional manifold of solutions in neural networks: insights from statistical physics
In these pedagogic notes I review the statistical mechanics approach to
neural networks, focusing on the paradigmatic example of the perceptron
architecture with binary an continuous weights, in the classification setting.
I will review the Gardner's approach based on replica method and the derivation
of the SAT/UNSAT transition in the storage setting. Then, I discuss some recent
works that unveiled how the zero training error configurations are
geometrically arranged, and how this arrangement changes as the size of the
training set increases. I also illustrate how different regions of solution
space can be explored analytically and how the landscape in the vicinity of a
solution can be characterized. I give evidence how, in binary weight models,
algorithmic hardness is a consequence of the disappearance of a clustered
region of solutions that extends to very large distances. Finally, I
demonstrate how the study of linear mode connectivity between solutions can
give insights into the average shape of the solution manifold.Comment: 22 pages, 9 figures, based on a set of lectures done at the "School
of the Italian Society of Statistical Physics", IMT, Lucc
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
Current activities at IITRI on high- temperature protective coatings
Heat resistant protective coatings for use in liquid propellant rocket engine
Structural and functional alterations of the cell nucleus in skeletal muscle wasting: the evidence in situ
The histochemical and ultrastructural analysis of the nuclear components involved in RNA transcription and splicing can reveal the occurrence of cellular dysfunctions eventually related to the onset of a pathological phenotype. In recent years, nuclear histochemistry at light and electron microscopy has increasingly been used to investigate the basic mechanisms of skeletal muscle diseases; the in situ study of nuclei of myofibres and satellite cells proved to be crucial for understanding the pathogenesis of skeletal muscle wasting in sarcopenia, myotonic dystrophy and laminopathies
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