Bell's inequalities and density matrices: revealing hidden nonlocality

As is well known, quantum mechanical behavior cannot, in general, be simulated by a local hidden variables model. Most -if not all- the proofs of this incompatibility refer to the correlations which arise when each of two (or more) systems separated in space is subjected to a single ideal measurement. This setting is good enough to show contradictions between local hidden variables models and quantum mechanics in the case of pure states. However, as shown here, it is not powerful enough in the case of mixtures. This is illustrated by an example. In this example, the correlations which arise when each of two systems separated in space is subjected to a single ideal measurement are classical; only when each system is subjected to a {\it sequence} of ideal measurements non-classical correlations are obtained. We also ask whether there are situations for which even this last procedure is not powerful enough and non-ideal measurements have to be considered as well

Analysis of Human Development Index In Sumatera Barat Province Using Biplot Method

The Human Development Index (HDI) is calculated from four variables, however, the HDI value cannot directly show which variables are superior in an area and which are not. For this reason, this study aims to analyze the strength of the HDI variables in each region in Sumatera Barat Province, using Biplot Analysis. Important findings resulted from biplot analysis indicate that the Sumatera Barat Province is categorized into five regional groups that are affected by the proximity value of its constituent variables. Out of the five groups, two groups are in an area not adjacent to the variable. The other two groups are in the variable area. While the last group is an extreme region compared to other regional groups. Areas that are not in the area of variables are weak against variables, while the area falling in the variable area is superior in the relevant variable. For extreme groups, Kota Padang is very superior in the adjusted per capita expenditure variable and superior in other variables too. Meanwhile, the Mentawai Islands Regency is very weak in all variables. Kota Padang Panjang is very superior in all variables of education but weak in the economic variable. The Biplot Analysis also revealed that Sijunjung Regency had a fairly good in expenditure, but it was not good enough in other dimensions of the HDI. Things like this are not given enough attention to ordinary HDI analysis, this is what makes the Biplot analysis important to do

Fixed speed competition on the configuration model with infinite variance degrees: equal speeds

We study competition of two spreading colors starting from single sources on the configuration model with i.i.d. degrees following a power-law distribution with exponent $\tau\in (2,3)$. In this model two colors spread with a fixed and equal speed on the unweighted random graph. We analyse how many vertices the two colors paint eventually. We show that coexistence sensitively depends on the initial local neighborhoods of the source vertices: if these neighborhoods are `dissimilar enough', then there is no coexistence, and the `loser' color paints a polynomial fraction of the vertices with a random exponent. If the local neighborhoods of the starting vertices are `similar enough', then there is coexistence, i.e., both colors paint a strictly positive proportion of vertices. We give a quantitative characterization of `similar' local neighborhoods: two random variables describing the double exponential growth of local neighborhoods of the source vertices must be within a factor $\tau-2$ of each other. Both of the two outcomes happen with positive probability with asymptotic value that is explicitly computable. This picture reinforces the common belief that location is an important feature in advertising. This paper is a follow-up of the similarly named paper that handles the case when the speeds of the two colors are not equal. There, we have shown that the faster color paints almost all vertices, while the slower color paints only a random sub-polynomial fraction of the vertices.Comment: 62 pages, 11 figure

Polynomials with and without determinantal representations

The problem of writing real zero polynomials as determinants of linear matrix polynomials has recently attracted a lot of attention. Helton and Vinnikov have proved that any real zero polynomial in two variables has a determinantal representation. Br\"and\'en has shown that the result does not extend to arbitrary numbers of variables, disproving the generalized Lax conjecture. We prove that in fact almost no real zero polynomial admits a determinantal representation; there are dimensional differences between the two sets. So the generalized Lax conjecture fails badly. The result follows from a general upper bound on the size of linear matrix polynomials. We then provide a large class of surprisingly simple explicit real zero polynomials that do not have a determinantal representation, improving upon Br\"and\'en's mostly unconstructive result. We finally characterize polynomials of which some power has a determinantal representation, in terms of an algebra with involution having a finite dimensional representation. We use the characterization to prove that any quadratic real zero polynomial has a determinantal representation, after taking a high enough power. Taking powers is thereby really necessary in general. The representations emerge explicitly, and we characterize them up to unitary equivalence

How Much Intraregional Exchange Rate Variability Could a Currency Union Remove? The Case of ASEAN+3

A multilateral currency union removes the intraregional exchange rates but not the union rate variability with the rest of the world. The intraregional exchange rate variability is thus latent. A two-step procedure is developed to measure the variability. The measured variables are used to model inflation and intraregional trade growth of individual union members. The resulting models form the base for counterfactual simulations of the union impact. Application to ASEAN+3 shows that the intraregional variability consists of mainly short-run shocks, which have significantly affected the inflation and trade growth of major ASEAN+3 members, and that a union would reduce inflation and promote intraregional trade on the whole but the benefits facing each member vary and may not be significant enough to warrant a vote for the union.Currency union, Latent variables, Dynamic factor model, Simulation

Central Bank Communication and Expectations Stabilization

This paper analyzes the value of communication in the implementation of monetary policy. The central bank is uncertain about the current state of the economy. Households and firms are uncertain about the statistical properties of aggregate variables, including nominal interest rates, and must learn about their dynamics using historical data. Given these uncertainties, when the central bank implements optimal policy, the Taylor principle is not sufficient for macroeconomic stability: for reasonable parameterizations self-fulfilling expectations are possible. To mitigate this instability, three communication strategies are contemplated: i) communicating the precise details of the monetary policy -- that is, the variables and coefficients; ii) communicating only the variables on which monetary policy decisions are conditioned; and iii) communicating the inflation target. The first two strategies restore the Taylor principle as a sufficient condition for stabilizing expectations. In contrast, in economies with persistent shocks, communicating the inflation target fails to protect against expectations driven fluctuations. These results underscore the importance of communicating the systematic component of monetary policy strategy: announcing an inflation target is not enough to stabilize expectations -- one must also announce how this target will be achieved.

A Diversification Operator for Genetic Algorithms

Conventional genetic algorithms suffer from a dependence on the initial generation used by the algorithm. In case the generation cosnsists of solutions which are not close enough to a global optimum but some of which are close to a relatively good local optimum, the algorithm is often guided a converge to the local optimum. In this paper, we provide a method which allows a genetic algorithm to search the solution space more effectively, and increases its chance to attain a global optimum. We provide computational experience with real-valued genetic algorithms on functions of two variables.