A nullstellensatz for sequences over F_p

Let p be a prime and let A=(a_1,...,a_l) be a sequence of nonzero elements in F_p. In this paper, we study the set of all 0-1 solutions to the equation a_1 x_1 + ... + a_l x_l = 0. We prove that whenever l >= p, this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for l < p. The critical case l=p is of particular interest. In this context, we prove that whenever l=p and A is nonconstant, the above equation has at least p-1 minimal 0-1 solutions, thus refining a theorem of Olson. The subcritical case l=p-1 is studied in detail also. Our approach is algebraic in nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper type theorem.Comment: 23 page

The history, evolution, and future of big data &amp; analytics:A bibliometric analysis of its relationship to performance in organizations

Big data and analytics (BDA) are gaining momentum, particularly in the practitioner world. Research linking BDA to improved organizational performance seems scarce and widely dispersed though, with the majority focused on specific domains and/or macro-level relationships. In order to synthesize past research and advance knowledge of the potential organizational value of BDA, the authors obtained a data set of 327 primary studies and 1252 secondary cited papers. This paper reviews this body of research, using three bibliometric methods. First, it elucidates its intellectual foundations via co-citation analysis. Second, it visualizes the historical evolution of BDA and performance research and its substreams through algorithmic historiography. Third, it provides insights into the field's potential evolution via bibliographic coupling. The results reveal that the academic attention for the BDA-performance link has been increasing rapidly. The study uncovered ten research clusters that form the field's foundation. While research seems to have evolved following two main, isolated streams, the past decade has witnessed more cross-disciplinary collaborations. Moreover, the study identified several research topics undergoing focused development, including financial and customer risk management, text mining and evolutionary algorithms. The review concludes with a discussion of the implications for different functional management domains and the gaps for both research and practice.</p

The H=xp model revisited and the Riemann zeros

Berry and Keating conjectured that the classical Hamiltonian H = xp is related to the Riemann zeros. A regularization of this model yields semiclassical energies that behave, in average, as the non trivial zeros of the Riemann zeta function. However, the classical trajectories are not closed, rendering the model incomplete. In this paper, we show that the Hamiltonian H = x (p + l_p^2/p) contains closed periodic orbits, and that its spectrum coincides with the average Riemann zeros. This result is generalized to Dirichlet L-functions using different self-adjoint extensions of H. We discuss the relation of our work to Polya's fake zeta function and suggest an experimental realization in terms of the Landau model.Comment: 5 pages, 3 figure

Spinful Composite Fermions in a Negative Effective Field

In this paper we study fractional quantum Hall composite fermion wavefunctions at filling fractions \nu = 2/3, 3/5, and 4/7. At each of these filling fractions, there are several possible wavefunctions with different spin polarizations, depending on how many spin-up or spin-down composite fermion Landau levels are occupied. We calculate the energy of the possible composite fermion wavefunctions and we predict transitions between ground states of different spin polarizations as the ratio of Zeeman energy to Coulomb energy is varied. Previously, several experiments have observed such transitions between states of differing spin polarization and we make direct comparison of our predictions to these experiments. For more detailed comparison between theory and experiment, we also include finite-thickness effects in our calculations. We find reasonable qualitative agreement between the experiments and composite fermion theory. Finally, we consider composite fermion states at filling factors \nu = 2+2/3, 2+3/5, and 2+4/7. The latter two cases we predict to be spin polarized even at zero Zeeman energy.Comment: 17 pages, 5 figures, 4 tables. (revision: incorporated referee suggestions, note added, updated references

Deciding the consistency of non-linear real arithmetic constraints with a conflict driven search using cylindrical algebraic coverings

We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real arithmetic. The algorithm is a variant of Cylindrical Algebraic Decomposition (CAD) adapted for satisfiability, where solution candidates (sample points) are constructed incrementally, either until a satisfying sample is found or sufficient samples have been sampled to conclude unsatisfiability. The choice of samples is guided by the input constraints and previous conflicts. The key idea behind our new approach is to start with a partial sample; demonstrate that it cannot be extended to a full sample; and from the reasons for that rule out a larger space around the partial sample, which build up incrementally into a cylindrical algebraic covering of the space. There are similarities with the incremental variant of CAD, the NLSAT method of Jovanovic and de Moura, and the NuCAD algorithm of Brown; but we present worked examples and experimental results on a preliminary implementation to demonstrate the differences to these, and the benefits of the new approach

An exact study of charge-spin separation, pairing fluctuations and pseudogaps in four-site Hubbard clusters

An exact study of charge-spin separation, pairing fluctuations and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature (T), magnetic field (h), on-site interaction (U) and chemical potential. Our results, near the average number of electrons =3, strongly suggest the existence of a critical parameter U_{c}(T) for the localization of electrons and a particle-hole binding (positive) gap at U>U_{c}(T), with a zero temperature quantum critical point, U_{c}(0)=4.584. For U<U_{c}(T), particle-particle pair binding is found with a (positive) pairing gap. The ground state degeneracy is lifted at U>U_c(T) and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers of electrons. In contrast, for U< U_c(T), we find an electron pair binding instability at finite temperature near =3, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. In addition, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich (=2), hole-poor (=4) and magnetic (=3) regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high T_c cuprates.Comment: 10 pages, 7 figure

Knowledge transfer within strategic partnerships: the case of HRM in the Brazilian motor industry supply chain

This paper investigates knowledge transfer (KT) of human resource management (HRM) across strategic partnerships in the Brazilian automotive industry, and the contextual factors impacting on KT within the supply chain. Case-study research in automotive companies and suppliers in Brazil is used to illustrate how in automotive industries, relationships with suppliers have traditionally been viewed as close, strategic partnerships, but over time, there has been a move towards more attenuated, supply chains, involving a shift towards more remote suppliers for basic components, and arms length relationships with them. In turn, this has impacted on how knowledge on HR has been transferred from manufacturers to suppliers. Both strategic partnerships and KT have been affected by internal drives towards cost cutting and talent retention, and external factors such as global competition through cheap imports, legislation, taxes, and unions. Evidence on the sometimes contradictory attitudes towards KT contributes towards the broader literatures on international HRM and KT in emerging economies, while the gradual unwinding of relationships has implications for policy and practice

The current progress of the ALICE Ring Imaging Cherenkov Detector

Recently, the last two modules (out of seven) of the ALICE High Momentum Particle Identification detector (HMPID) were assembled and tested. The full detector, after a pre-commissioning phase, has been installed in the experimental area, inside the ALICE solenoid, at the end of September 2006. In this paper we review the status of the ALICE/HMPID project and we present a summary of the series production of the CsI photo-cathodes. We describe the key features of the production procedure which ensures high quality photo-cathodes as well as the results of the quality assessment performed by means of a specially developed 2D scanner system able to produce a detailed map of the CsI photo-current over the entire photo-cathode surface. Finally we present our recent R&D efforts toward the development of a novel generation of imaging Cherenkov detectors with the aim to identify, in heavy ions collisions, hadrons up to 30 GeV/c.Comment: Presented at the Imaging-2006 Conference, Stockholm, Sweden, June 200

Investigating knowledge management factors affecting Chinese ICT firms performance: An integrated KM framework

This is an Author's Accepted Manuscript of an article published in the Journal of Information Systems Management, 28(1), 19 - 29, 2011, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/10580530.2011.536107.This article sets out to investigate the critical factors of Knowledge Management (KM) which are considered to have an impact on the performance of Chinese information and communication technology (ICT) firms. This study confirms that the cultural environment of an enterprise is central to its success in the context of China. It shows that a collaborated, trusted, and learning environment within ICT firms will have a positive impact on their KM performance