Search results for "Open problem"
showing 10 items of 37 documents
Universality of Schmidt decomposition and particle identity
2017
Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, it is held not to exist for identical particles, an open problem forbidding its application to analyze such many-body quantum systems. Here we prove, using a newly developed approach, that the Schmidt decomposition exists for identical particles and is thus universal. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in sep…
Unbiased Branches: An Open Problem
2007
The majority of currently available dynamic branch predictors base their prediction accuracy on the previous k branch outcomes. Such predictors sustain high prediction accuracy but they do not consider the impact of unbiased branches, which are difficult-to-predict. In this paper, we evaluate the impact of unbiased branches in terms of prediction accuracy on a range of branch difference predictors using prediction by partial matching, multiple Markov prediction and neural-based prediction. Since our focus is on the impact that unbiased branches have on processor performance, timing issues and hardware costs are out of scope of this investigation. Our simulation results, with the SPEC2000 in…
An experimental study of the stability problem in discrete tomography
2003
This paper introduces the topic of discrete tomography, briefly showing its main applications, algorithms and new prospects of research. It focuses on the still open problem of stability, facing it from an experimental point of view. In particular an extensive simulation lets verify the robustness of a well known reconstruction technique for binary convex objects, calculating the probability of finding solutions compatible with a given set of noisy projections. © 2005 Elsevier Ltd. All rights reserved.
On the size of the set of unbounded multilinear operators between Banach spaces
2020
Among other results we investigate $\left( \alpha,\beta\right) $-lineability of the set of non-continuous $m$-linear operators defined between normed spaces as a subset of the space of all $m$-linear operators. We also give a partial answer to an open problem on the lineability of the set of non absolutely summing operators.
More restrictive Gray codes for necklaces and Lyndon words
2008
In the last years, the order induced by the Binary Reflected Gray Code or its generalizations shown an increasing interest. In this note we show that the BRGC order induces a cyclic 2-Gray code on the set of binary necklaces and Lyndon words and a cyclic 3-Gray code on the unordered counterparts. This is an improvement and a generalization to unlabeled words of the result in [V. Vajnovszki, Gray code order for Lyndon words, Discrete Math. Theoret. Comput. Sci. 9 (2) (2007) 145-152; M. Weston, V. Vajnovszki, Gray codes for necklaces and Lyndon words of arbitrary base, Pure Mathematics and Applications/Algebra and Theoretical Computer Science, in press]; however an algorithmic implementation …
New Algorithms for Computing Phylogenetic Biodiversity
2014
A common problem that appears in many case studies in ecology is the following: given a rooted phylogenetic tree \(\mathcal{T}\) and a subset R of its leaf nodes, we want to compute the distance between the elements in R. A very popular distance measure that can be used for this reason is the Phylogenetic Diversity (PD), which is defined as the cost of the minimum weight Steiner tree in \(\mathcal{T}\) that spans the nodes in R. To analyse the value of the PD for a given set R it is important also to calculate the variance of this measure. However, the best algorithm known so far for computing the variance of the PD is inefficient; for any input tree \(\mathcal{T}\) that consists of n nodes…
Conformal Symmetry and Feynman Integrals
2018
Singularities hidden in the collinear region around an external massless leg may lead to conformal symmetry breaking in otherwise conformally invariant finite loop momentum integrals. For an $\ell$-loop integral, this mechanism leads to a set of linear $2$nd-order differential equations with a non-homogeneous part. The latter, due to the contact nature of the anomaly in momentum space, is determined by $(\ell-1)$-loop information. Solving such differential equations in general is an open problem. In the case of 5-particle amplitudes up to two loops, the function space is known, and we can thus follow a bootstrap approach to write down the solution. As a first application of this method, we …
Dynamics for a simple graph using the U(N) framework for loop quantum gravity
2012
The implementation of the dynamics in loop quantum gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We find an interesting global U(N) symmetry in this model that selects the homogeneous/isotropic sector. Then, we propose a quantum Hamiltonian operator for this reduced sector. Finally, we introduce the spinor representation for LQG in order to propose a classical effective dynamics for this model.
A note on the computation of geometrically defined relative velocities
2011
We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike Fermi and astrometric relative velocities, that also depend on the acceleration of the observer and the corresponding relative position of the test particle, but only at the event of observation and not around it, as it would be deduced, in principle, from the definition of these velocities. Finally, we propose an open problem in general relativity that consists on finding intr…
Non-cooperative Equilibria of Fermi Systems With Long Range Interactions
2019
We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, we give a first answer to an old open problem in mathematical physics - first addressed by Ginibre in 1968 within a different context - about the validity of the so-called Bogoliubov approximation on the level of states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, our method provides a systematic way to study all its correlation functions and can thus be used to analyze the physics of long range interactions. Furthermore, we show tha…