Encoding databases satisfying a given set of dependencies

Consider a relation schema with a set of dependency constraints. A fundamental question is what is the minimum space where the possible instances of the schema can be "stored". We study the following model. Encode the instances by giving a function which maps the set of possible instances into the set of words of a given length over the binary alphabet in a decodable way. The problem is to find the minimum length needed. This minimum is called the information content of the database. We investigate several cases where the set of dependency constraints consist of relatively simple sets of functional or multivalued dependencies. We also consider the following natural extension. Is it possible to encode the instances such a way that small changes in the instance cause a small change in the code. © 2012 Springer-Verlag

Hmm-based monitoring of packet channels

Abstract. Performance of real-time applications on network communication channels are strongly related to losses and temporal delays. Several studies showed that these network features may be correlated and exhibit a certain degree of memory such as bursty losses and delays. The memory and the statistical dependence between losses and temporal delays suggest that the channel may be well modelled by a Hidden Markov Model (HMM) with appropriate hidden variables that capture the current state of the network. In this paper we discuss on the effectiveness of using an HMM to model jointly loss and delay behavior of real communication channel. Excellent performance in modelling typical channel behavior in a set of real packet links are observed. The system parameters are found via a modified version of the EM algorithm. Hidden state analysis shows how the state variables characterize channel dynamics. State-sequence estimation is obtained by use of the Viterbi algorithm. Real-time modelling of the channel is the first step to implement adaptive communication strategies.

Preinfection in vitro chemotaxis, phagocytosis, oxidative burst, and expression of CD11/CD18 receptors and their predictive capacity on the outcome of mastitis induced in dairy cows with Escherichia coli.

Four to 6 wk after parturition, 12 cows in second, fourth, or fifth lactation were experimentally infected in one gland with Escherichia coli. The capacity of chemotaxis, phagocytosis, oxidative burst, and expression of CD11/CD18 receptors to predict the severity of IMI was measured. Bacterial counts in the infected quarter, expressed as area under the curve, and residual milk production in the uninfected quarters were compared to determine severity of the infection. Although these two outcome parameters were highly negatively correlated, regression models with preinfection tests for leukocyte function fitted best with bacterial counts as an outcome parameter. Of the preinfection tests for leukocyte function, chemotaxis best predicted the outcome of the IMI that had been experimentally induced by E. coli. The number of circulating peripheral leukocytes just prior to inoculation was used to predict 52 and 45% of the severity of IMI for bacterial counts and residual milk production, respectively. As a categorical variable, parity predicted 75 and 56% of the severity of IMI expressed as bacterial counts and residual milk production, respectively. Because of the strong effect of parity on the outcome of the experimentally induced mastitis, analysis was performed to discriminate between second parity cows and older cows. Significant differences were found for the number of circulating peripheral leukocytes and for the expression of CD11b/CDl8 and CD11c/CD18 receptors between younger and older cows

Clones with finitely many relative R-classes

For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A iff each one is a substitution instance of the other using operations from C. We study the clones for which there are only finitely many relative R-classes.Comment: 41 pages; proofs improved, examples adde

Evolution models for mass transportation problems

We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in [5], where a suitable cost functional $F(\rho,v)$, depending on the density $\rho$ and on the velocity $v$ (which fulfill the continuity equation), has to be minimized. Acting on the functional $F$ various forms of mass transportation problems can be modeled, as for instance those presenting congestion effects, occurring in traffic simulations and in crowd motions, or concentration effects, which give rise to branched structures.Comment: 16 pages, 14 figures; Milan J. Math., (2012

Quantum capacity under adversarial quantum noise: arbitrarily varying quantum channels

We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In he final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2 and arXiv:1010.0418. Published "Online First" in Communications in Mathematical Physics, 201

Aalenian to Cenomanian Radiolaria of the Bermeja Complex (Puerto Rico) and Pacific origin of radiolarites on the Caribbean Plate

The study of the radiolarian ribbon chert is a key in determining the origins of associated Mesozoic oceanic terranes and may help to achieve a general agreement regarding the basic principles on the evolution of the Caribbean Plate. The Bermeja Complex of Puerto Rico, which contains serpentinized peridotite, altered basalt, amphibolite, and chert (Mariquita Chert Formation), is one of these crucial oceanic terranes. The radiolarian biochronology presented in this work is mainly based by correlation on the biozonations of Baumgartner et al. (1995) and O'Dogherty (1994) and indicates an early Middle Jurassic to early Late Cretaceous (late Bajocian-early Callovian to late early Albian-early middle Cenomanian) age. The illustrated assemblages contain about 120 species, of which one is new (Pantanellium karinae), and belonging to about 50 genera. A review of the previous radiolarian published works on the Mariquita Chert Formation and the results of this study suggest that this formation ranges in age from Middle Jurassic to early Late Cretaceous (late Aalenian to early-middle Cenomanian) and also reveal a possible feature of the Bermeja Complex, which is the younging of radiolarian cherts from north to south, evoking a polarity of accretion. On the basis of a currently exhaustive inventory of the radiolarite facies s.s. on the Caribbean Plate, a re-examination of the regional distribution of Middle Jurassic sediments associated with oceanic crust, and a paleoceanographic argumentation on the water currents, we come to the conclusion that the radiolarite and associated Mesozoic oceanic terranes of the Caribbean Plate are of Pacific origin. Eventually, a discussion on the origin of the cherts of the Mariquita Formation illustrated by Middle Jurassic to middle Cretaceous geodynamic models of the Pacific and Caribbean realms bring up the possibility that the rocks of the Bermeja Complex are remnants of two different oceans

Class of correlated random networks with hidden variables

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an \textit{a priori} specified correlation structure. We also present an extension of the class, to map non-equilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system

What is the Nature of EUV Waves? First STEREO 3D Observations and Comparison with Theoretical Models

One of the major discoveries of the Extreme ultraviolet Imaging Telescope (EIT) on SOHO were intensity enhancements propagating over a large fraction of the solar surface. The physical origin(s) of the so-called `EIT' waves is still strongly debated. They are considered to be either wave (primarily fast-mode MHD waves) or non-wave (pseudo-wave) interpretations. The difficulty in understanding the nature of EUV waves lies with the limitations of the EIT observations which have been used almost exclusively for their study. Their limitations are largely overcome by the SECCHI/EUVI observations on-board the STEREO mission. The EUVI telescopes provide high cadence, simultaneous multi-temperature coverage, and two well-separated viewpoints. We present here the first detailed analysis of an EUV wave observed by the EUVI disk imagers on December 07, 2007 when the STEREO spacecraft separation was $\approx 45^\circ$. Both a small flare and a CME were associated with the wave cadence, and single temperature and viewpoint coverage. These limitations are largely overcome by the SECCHI/EUVI observations on-board the STEREO mission. The EUVI telescopes provide high cadence, simultaneous multi-temperature coverage, and two well-separated viewpoints. Our findings give significant support for a fast-mode interpretation of EUV waves and indicate that they are probably triggered by the rapid expansion of the loops associated with the CME.Comment: Solar Physics, 2009, Special STEREO Issue, in pres