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Entanglement Entropy of Quantum Wire Junctions
No full textWe consider a fermion gas on a star graph modeling a quantum wire junction
and derive the entanglement entropy of one edge with respect to the rest of the
junction. The gas is free in the bulk of the graph, the interaction being
localized in its vertex and described by a non-trivial scattering matrix. We
discuss all point-like interactions, which lead to unitary time evolution of
the system. We show that for a finite number of particles N, the Renyi
entanglement entropies of one edge grow as ln N with a calculable prefactor,
which depends not only on the central charge, but also on the total
transmission probability from the considered edge to the rest of the graph.
This result is extended to the case with an harmonic potential in the bulk
On the cohomology of almost-complex manifolds
No full textFollowing [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T.-J. Li and W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.17(4) (2009) 651–683] and the results obtained by [D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math.36(1) (1976) 225–255] to study the cone of semi-Kähler structures on a compact semi-Kähler manifold
Network Conscious pi-calculus
No full textTraditional process calculi usually abstract away from network details, modeling only communication over shared channels. They, however, seem inadequate to describe new network architectures, such as Software Defined Networks, where programs are allowed to manipulate the infrastructure. In this paper we present a network conscious, proper extension of the pi-calculus: we add connector names and the primitives to handle them, and we provide both an interleaving and a concurrent semantics. The extension to connector names is natural and seamless, since they are handled in full analogy with ordinary names. In the interleaving case, observations are the routing paths through which sent and received data are transported, while in the concurrent case we allow to observe multisets of paths. However, restricted connector names do not appear in the observations, which thus can possibly be as abstract as in the pi-calculus. Finally, for the concurrent semantics we show that bisimilarity is a congruence, and this property holds also for the concurrent version of the pi-calculus
Merawti: a method for the ranking of the alternatives with ties
No full textIn this technical report we present a method that can be used by a set of decison makers in order to rank a certain number of alternatives according to a given set of criteria. The method aims at producing a directed multigraph involving all the alternatives so that it is possible for the decison makers to identify the worst alternatives and the best alternatives. The worst alternatives are never selected by the decision makers that perform their final selection among teh best aletrnatives. <br /
Compressed static functions with applications to other dictionary problems\vspace
No full textGiven a set of integer keys from a bounded universe along with associated data, the dictionary problem asks to answer two queries: membership and retrieval. Membership has to tell whether a given element is in the dictionary or not; retrieval has to return the data associated with the searched key.
This paper studies three well-established relaxations of this basic problem: (Compressed) Static functions, Approximate membership and Relative membership.
(Compressed) Static functions. In this relaxation, also known as retrieval-only dictionaries, we are given a set of integers and each of them has associated data from an alphabet of size . The problem asks to build a dictionary that, given a key , returns its associate data. Notice that, whenever , arbitrary data is returned.
This problem has been widely studied in the past.
Solutions to this problem have to carefully organize associated data, so that, they can be retrieved in constant time without the need of storing keys in .
Compressed static functions move a step forward: not only do not store the keys, but also achieve space complexities bounded in term of the entropy of the associated data.
Such kind of solutions are very interesting mainly for two reasons. Firstly, being at most , these results are always at least as good as the uncompressed ones. Moreover, since the associated data often follow a skewed distribution, could even become sublinear in .
The current best solutions are by Porat and Hreinsson et al. The first one requires bits of space, while the second one uses bits of space, where is the probability of the most frequent symbol and is a constant greater than . Thus, the space complexities of these solutions are incomparable:
the former has a sublinear overhead but is not compressed, while the latter is suboptimal due to the factor to multiply and has an overhead that may be depending on .
Our optimal scheme achieves the best of the two being the first known solution obtaining simultaneously constant query time, compressed space (), and sublinear overhead ().
We strongly believe that these characteristics makes the use of static functions significantly more appealing for many applications.
Approximate membership. The approximate membership problem has been studied for decades and the Bloom filter data structure~is probably the most popular and widely used technique solving it.
With Bloom filters we can represent a set of integers by using bits of space with false positive probability ({\sf fpp}) .
Both its space and time complexities are non-optimal: space is a constant factor away from optimal, and query time is logarithmic in .
Constant time approximate membership data structures are able to achieve optimal bits of space only if
is a power of two.
The current best solution requires an bits overhead in addition to the optimal space, for an arbitrary {\sf fpp}.
Our optimal scheme is the first known solution having overhead, for any value of such that , namely, any reasonable choice of in practice.
Relative membership. This problem asks to solve a further relaxation of the membership query. Given two sets and with , we must be able to distinguish whether a key belongs to or . Our compressed static functions are used to obtain a constant time solution for the problem achieving an optimal space complexity (up to lower order term)
Services selection and composition in Opportunistic Networks
No full textOpportunistic computing is an exciting evolution of opportunistic networks.
The services provision in these networks suffer from the limitations of conventional MANETs such as non stable
connections and limited distribution of knowledge between nodes.
The introduction of services composition introduces new challenges for the definition
of a system able to recognize the best alternative to choose from.
The nodes in the network have heterogeneous physical characteristics, different mobility patterns and executes a variety of different services.
During the connection, pairs of nodes may collaborate by exchanging information on the network status, such as
characteristics of the encountered nodes and workload of their nodes.
We propose a system which is capable of processing such information in order to offer the best alternative for a service request.
The selection algorithms evaluate services composition by considering alternative paths.
In this paper we analyze two types of knowledge distribution strategies to study sequential compositions in opportunistic networks.
We propose an analytical model which is validated through a set of simulations, verifying the properties set
Generalized Bundle Methods for Sum-Functions with "Easy" Components: Applications to Multicommodity Network Design
No full textWe propose a version of the (generalized) bundle scheme for convex nondifferentiable optimization suitable for the case of a sum-function where some of the components are "easy", that is, they are Lagrangian functions of explicitly known compact convex programs. This corresponds to a stabilized partial Dantzig-Wolfe decomposition, where suitably modified representations of the "easy" convex subproblems are inserted in the master problem as an alternative to iteratively inner-approximating them by extreme points, thus providing the algorithm with exact information about a part of the dual objective function. The resulting master problems are potentially larger and less well-structured than the standard ones, ruling out the available specialized techniques and requiring the use of general-purpose solvers for their solution; this strongly favors piecewise-linear stabilizing terms, as opposed to the more usual quadratic ones. This in turn may have an adverse effect on the convergence speed of the algorithm, so that the overall performance may depend on appropriate tuning of all these aspects. Yet, very good computational results are obtained in at least one relevant application: the computation of tight lower bounds for Fixed-Charge Multicommodity Min-Cost Flow problems. <br /
Particular order
No full textThis technical report presents a new partial order of a set A of alternatives according to a set of criteria C.The order is based on a binary strict preference relation that is not transitive but that satisfies asymmetry.
The order corresponds to a directed graph as an aiding tool to allow the single decision maker to select the best alternative from the set A
On the time dependence of the -index
No full textSUMMARY The time dependence of the -index is analyzed by considering the average
behaviour of as a function of the academic age for about 1400 Italian
physicists, with career lengths spanning from 3 to 46 years. The individual
-index is strongly correlated with the square root of the total citations
: . For academic ages ranging from 12 to 24
years, the distribution of the time scaled index is
approximately time-independent and it is well described by the Gompertz
function. The time scaled index has an average approximately
equal to 3.8 and a standard deviation approximately equal to 1.6. Finally, the
time scaled index appears to be strongly correlated with the
contemporary -index
The disorder parameter of dual superconductivity in QCD revisited
No full textWe discover the origin of the pathologies of the disorder parameter used in
previous papers to detect dual superconductivity of QCD vacuum, and we remove
them by defining an improved disorder parameter. A check of the approach is
made by numerical simulations of SU(2) gauge theory, which demonstrate that the
approach is consistent and with it that deconfinement is a transition from dual
superconductor to normal