Quantum Interactive Proofs with Competing Provers

This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language having an ordinary quantum interactive proof system also has a quantum refereed game in which the verifier exchanges just one round of messages with each prover. A key part of our proof is the fact that there exists a single quantum measurement that reliably distinguishes between mixed states chosen arbitrarily from disjoint convex sets having large minimal trace distance from one another. We also show how to reduce the probability of error for some classes of quantum refereed games.Comment: 13 pages, to appear in STACS 200

A Perturbative Construction of Lattice Chiral Fermions

We perform a renormalization group transformation to construct a lattice theory of chiral fermions. The field variables of the continuum theory are averaged over hypercubes to define lattice fields. Integrating out the continuum variables in perturbation theory we derive a chirally invariant effective action for the lattice fields. This is consistent with the Nielsen-Niniomiya theorem because the effective action is nonlocal. We also construct the axial current on the lattice and we show that the axial anomaly of the continuum theory is reproduced in the Schwinger model. This shows that chiral fermions can be regularized on the lattice.Comment: 8 pages, LaTe

Conserved Quantities in f(R)f(R) Gravity via Noether Symmetry

This paper is devoted to investigate $f(R)$ gravity using Noether symmetry approach. For this purpose, we consider Friedmann Robertson-Walker (FRW) universe and spherically symmetric spacetimes. The Noether symmetry generators are evaluated for some specific choice of $f(R)$ models in the presence of gauge term. Further, we calculate the corresponding conserved quantities in each case. Moreover, the importance and stability criteria of these models are discussed.Comment: 14 pages, accepted for publication in Chin. Phys. Let

QCD as a Quantum Link Model

QCD is constructed as a lattice gauge theory in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. The resulting quantum link model for QCD is formulated with a fifth Euclidean dimension, whose extent resembles the inverse gauge coupling of the resulting four-dimensional theory after dimensional reduction. The inclusion of quarks is natural in Shamir's variant of Kaplan's fermion method, which does not require fine-tuning to approach the chiral limit. A rishon representation in terms of fermionic constituents of the gluons is derived and the quantum link Hamiltonian for QCD with a U(N) gauge symmetry is expressed in terms of glueball, meson and constituent quark operators. The new formulation of QCD is promising both from an analytic and from a computational point of view.Comment: 27 pages, including three figures. ordinary LaTeX; Submitted to Nucl. Phys.

On the Threshold of Intractability

We study the computational complexity of the graph modification problems Threshold Editing and Chain Editing, adding and deleting as few edges as possible to transform the input into a threshold (or chain) graph. In this article, we show that both problems are NP-complete, resolving a conjecture by Natanzon, Shamir, and Sharan (Discrete Applied Mathematics, 113(1):109--128, 2001). On the positive side, we show the problem admits a quadratic vertex kernel. Furthermore, we give a subexponential time parameterized algorithm solving Threshold Editing in $2^{O(\surd k \log k)} + \text{poly}(n)$ time, making it one of relatively few natural problems in this complexity class on general graphs. These results are of broader interest to the field of social network analysis, where recent work of Brandes (ISAAC, 2014) posits that the minimum edit distance to a threshold graph gives a good measure of consistency for node centralities. Finally, we show that all our positive results extend to the related problem of Chain Editing, as well as the completion and deletion variants of both problems

The role of climate, water and biotic interactions in shaping biodiversity patterns in arid environments across spatial scales

This is the final version. Available on open access from Wiley via the DOI in this recordData availability: Maxent species distribution modelling outputs and R scripts for running the GLMMs available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.f8c0c8hAim: Desert ecosystems, with their harsh environmental conditions, hold the key to understanding the responses of biodiversity to climate change. As desert community structure is influenced by processes acting at different spatial scales, studies combining multiple scales are essential for understanding the conservation requirements of desert biota. We investigated the role of environmental variables and biotic interactions in shaping broad and fine-scale patterns of diversity and distribution of bats in arid environments to understand how the expansion of nondesert species can affect the long-term conservation of desert biodiversity. Location: Levant, Eastern Mediterranean. Methods: We combine species distribution modelling and niche overlap statistics with a statistical model selection approach to integrate interspecific interactions into broadscale distribution models and fine-scale analysis of ecological requirements. We focus on competition between desert bats and mesic species that recently expanded their distribution into arid environment following anthropogenic land-use changes. Results: We show that both climate and water availability limit bat distributions and diversity across spatial scales. The broadscale distribution of bats was determined by proximity to water and high temperatures, although the latter did not affect the distribution of mesic species. At the fine-scale, high levels of bat activity and diversity were associated with increased water availability and warmer periods. Desert species were strongly associated with warmer and drier desert types. Range and niche overlap were high among potential competitors, but coexistence was facilitated through fine-scale spatial partitioning of water resources. Main conclusions: Adaptations to drier and warmer conditions allow desert-obligate species to prevail in more arid environments. However, this competitive advantage may disappear as anthropogenic activities encroach further into desert habitats. We conclude that reduced water availability in arid environments under future climate change projections pose a major threat to desert wildlife because it can affect survival and reproductive success and may increase competition over remaining water resources.Ministry of Environmental Protection of IsraelNatural Environment Research Council (NERC

Quantum Spins and Quantum Links: The D-Theory Approach to Field Theory

A new non-perturbative approach to quantum field theory is proposed. Instead of performing a path integral over configurations of classical fields, D-theory works with discrete quantized variables. Classical spin fields are replaced by quantum spins, and classical gauge fields are replaced by quantum links. The classical fields of a d-dimensional quantum field theory reappear as low-energy effective degrees of freedom of the discrete variables, provided the (d+1)-dimensional D-theory is massless. When the extent of the extra Euclidean dimension becomes small in units of the correlation length, an ordinary d-dimensional quantum field theory emerges by dimensional reduction. The D-theory formulation of some spin models and gauge theories is constructed explicitly. In particular, QCD emerges as a quantum link model.Comment: LATTICE98(plenary talk

Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a $\Pi\Sigma\Pi$ polynomial. We first prove that the first problem is \#P-hard and then devise a $O^*(3^ns(n))$ upper bound for this problem for any polynomial represented by an arithmetic circuit of size $s(n)$. Later, this upper bound is improved to $O^*(2^n)$ for $\Pi\Sigma\Pi$ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for $\Pi\Sigma$ polynomials. On the negative side, we prove that, even for $\Pi\Sigma\Pi$ polynomials with terms of degree $\le 2$, the first problem cannot be approximated at all for any approximation factor $\ge 1$, nor {\em "weakly approximated"} in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time $\lambda$-approximation algorithm for $\Pi\Sigma\Pi$ polynomials with terms of degrees no more a constant $\lambda \ge 2$. On the inapproximability side, we give a $n^{(1-\epsilon)/2}$ lower bound, for any $\epsilon >0,$ on the approximation factor for $\Pi\Sigma\Pi$ polynomials. When terms in these polynomials are constrained to degrees $\le 2$, we prove a $1.0476$ lower bound, assuming $P\not=NP$; and a higher $1.0604$ lower bound, assuming the Unique Games Conjecture

Optimal locations of groundwater extractions in coastal aquifers

A regional water supply management model for coastal aquifers was developed. One of its outcomes is the definition of the optimized locations for groundwater withdrawal. Such a tool permits the analysis of alternative plans for groundwater extraction and the sustainable use of water resources in a coastal aquifer subject to saltwater intrusion. The principal components are the evolutionary optimization and the analytical/numerical simulation models. The optimization technique looks for the best well locations taking into consideration the economic results and the satisfaction of the societal water demand. However these two concerns are conditioned by trying to control the saltwater intrusion, i.e., preserving the environmental equilibrium. The simulation model uses the governing mathematical equations for groundwater movement to find the interface between freshwater and saltwater. Because of the non-linearity in the system and the possibility of a jumping interface, a security distance was defined. This is a controlling variable which can be set by the decision makers. The model was applied to a typical case with interesting results. For example, diagrams showing the relationship between the location of the wells and the security distance(s) are of importance to the managers. It was also crucial to have an understanding of the tradeoffs between groundwater withdrawals, positions of the wells from the coast line, and the security distance. The model was also applied to a real case in order to relate the extractions, distances and artificial recharge (not presented in this paper).Civil Engineering Research Centre of the University of Minho.Science and Technology Foundation -POCTI/ECM/2512/9