ASPECTS REGARDING THE FINANCING OF HIGHER EDUCATION

This paper sets forth the issue of financing higher education in Romania according tothe fundamental principles adopted by most of the countries of the European Union. Under suchcircumstances, the two components of financing State universities are minutely exhibited, namelybasic financing and complementary financing. At the same time, the extremely important matterrequiring the foundation of an efficient and competitive educational system demanded by the newenvironment also implies the providing of financing resources and the implementation of amanagement that allows a good administration and an efficient use of the funds.basic financing, complementary financing, State higher education, university autonomy.

The Implications of the Adherence to the European Union over the Achievementof a Functional Market Economy in Romania

The transition to the economy with competitive market intersects in a good measure with the adherence of Romania to the European Union. We take into account both the preparation period of the conditions of pre-adherence, when between Romania and the European Union functioned an Agreement of association, and also the period after the formal official adherence on the 1st of January 2007. Romania’s adherence to the European Union has special implications over the achievement of a functional market economy through the assimilation of the communitarian acquis, especially in the competence field but also through the perspective of the introduction of the unique currency Euro. The benefic effects started to manifest even since the moment of the signing of the Association Agreement, through financial assistance of which Romania beneficiated. The adherence perspective obliged Romania to adept properly the business medium and to improve the macroeconomic stability. The communitarian aquis must be assimilated in its integrity, not an easy thing, especially if we take into account that this is also affected by a certain dynamism due to the changes produced in the European space. The alignment to the European structures means the reformation on new coordinates of all the components of the socio-economic and politic life. The corollary of all these transformations and efforts is the Romanians’ status of European citizens.The adherence to the European Union, Macroeconomic, the competition’s policy.

ASPECTS REGARDING THE INTERDEPENDENCE BETWEEN AGGREGATED DEMAND AND OFFER

The paper focuses upon aggregated demand and offer and their interdependence asfundamental variables of competition market determining both the balance level of the generalindex of prices and the balance level of national production. Several forms of the correlationbetween aggregated demand and offer having significant consequences are also emphasized as wellas the balance between them.aggregated demand and offer, general level of prices, national production.

Sharp Bounds for Optimal Decoding of Low Density Parity Check Codes

Consider communication over a binary-input memoryless output-symmetric channel with low density parity check (LDPC) codes and maximum a posteriori (MAP) decoding. The replica method of spin glass theory allows to conjecture an analytic formula for the average input-output conditional entropy per bit in the infinite block length limit. Montanari proved a lower bound for this entropy, in the case of LDPC ensembles with convex check degree polynomial, which matches the replica formula. Here we extend this lower bound to any irregular LDPC ensemble. The new feature of our work is an analysis of the second derivative of the conditional input-output entropy with respect to noise. A close relation arises between this second derivative and correlation or mutual information of codebits. This allows us to extend the realm of the interpolation method, in particular we show how channel symmetry allows to control the fluctuations of the overlap parameters.Comment: 40 Pages, Submitted to IEEE Transactions on Information Theor

The adaptive interpolation method for proving replica formulas. Applications to the Curie-Weiss and Wigner spike models

In this contribution we give a pedagogic introduction to the newly introduced adaptive interpolation method to prove in a simple and unified way replica formulas for Bayesian optimal inference problems. Many aspects of this method can already be explained at the level of the simple Curie-Weiss spin system. This provides a new method of solution for this model which does not appear to be known. We then generalize this analysis to a paradigmatic inference problem, namely rank-one matrix estimation, also refered to as the Wigner spike model in statistics. We give many pointers to the recent literature where the method has been succesfully applied

Extended Edge States in Finite Hall Systems

We study edge states of a random Schroedinger operator for an electron submitted to a magnetic field in a finite macroscopic two dimensional system of linear dimensions equal to L. The y direction is L-periodic and in the x direction the electron is confined by two smoothly increasing parallel boundary potentials. We prove that, with large probability, for an energy range in the first spectral gap of the bulk Hamiltonian, the spectrum of the full Hamiltonian consists only on two sets of eigenenergies whose eigenfuntions have average velocities which are strictly positive/negative, uniformly with respect to the size of the system. Our result gives a well defined meaning to the notion of edge states for a finite cylinder with two boundaries, and extends previous studies on systems with only one boundary.Comment: 24 pages, 1 figure; Submitte

Applications of correlation inequalities to low density graphical codes

This contribution is based on the contents of a talk delivered at the Next-SigmaPhi conference held in Crete in August 2005. It is adressed to an audience of physicists with diverse horizons and does not assume any background in communications theory. Capacity approaching error correcting codes for channel communication known as Low Density Parity Check (LDPC) codes have attracted considerable attention from coding theorists in the last decade. Surprisingly strong connections with the theory of diluted spin glasses have been discovered. In this work we elucidate one new connection, namely that a class of correlation inequalities valid for gaussian spin glasses can be applied to the theoretical analysis of LDPC codes. This allows for a rigorous comparison between the so called (optimal) maximum a posteriori and the computationaly efficient belief propagation decoders. The main ideas of the proofs are explained and we refer to recent works for the more lengthy technical details.Comment: 11 pages, 3 figure

The Velocity of the Propagating Wave for General Coupled Scalar Systems

We consider spatially coupled systems governed by a set of scalar density evolution equations. Such equations track the behavior of message-passing algorithms used, for example, in coding, sparse sensing, or constraint-satisfaction problems. Assuming that the "profile" describing the average state of the algorithm exhibits a solitonic wave-like behavior after initial transient iterations, we derive a formula for the propagation velocity of the wave. We illustrate the formula with two applications, namely Generalized LDPC codes and compressive sensing.Comment: 5 pages, 5 figures, submitted to the Information Theory Workshop (ITW) 2016 in Cambridge, U

Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation

We investigate an encoding scheme for lossy compression of a binary symmetric source based on simple spatially coupled Low-Density Generator-Matrix codes. The degree of the check nodes is regular and the one of code-bits is Poisson distributed with an average depending on the compression rate. The performance of a low complexity Belief Propagation Guided Decimation algorithm is excellent. The algorithmic rate-distortion curve approaches the optimal curve of the ensemble as the width of the coupling window grows. Moreover, as the check degree grows both curves approach the ultimate Shannon rate-distortion limit. The Belief Propagation Guided Decimation encoder is based on the posterior measure of a binary symmetric test-channel. This measure can be interpreted as a random Gibbs measure at a "temperature" directly related to the "noise level of the test-channel". We investigate the links between the algorithmic performance of the Belief Propagation Guided Decimation encoder and the phase diagram of this Gibbs measure. The phase diagram is investigated thanks to the cavity method of spin glass theory which predicts a number of phase transition thresholds. In particular the dynamical and condensation "phase transition temperatures" (equivalently test-channel noise thresholds) are computed. We observe that: (i) the dynamical temperature of the spatially coupled construction saturates towards the condensation temperature; (ii) for large degrees the condensation temperature approaches the temperature (i.e. noise level) related to the information theoretic Shannon test-channel noise parameter of rate-distortion theory. This provides heuristic insight into the excellent performance of the Belief Propagation Guided Decimation algorithm. The paper contains an introduction to the cavity method