Industrial Clustering and the Returns to Inventive Activity Canadian Biotechnology Firms, 1991-2000

We examine how industrial clustering affects biotechnology firms’ innovativeness, contrasting similar firms not located in clusters or located in clusters that are or are not focused on the firm’s technological specialization. Using detailed firm level data, we find clustered firms are eight times more innovative than geographically remote firms, with largest effects for firms located in clusters strong in their own specialization. For firms located in a cluster strong in their specialization we also find that R&D productivity is enhanced by a firm’s own R&D alliances and also by the R&D alliances of other colocated firms.Biotechnology, industrial clustering, knowledge spillovers, R&D productivity, strategic alliances

Spectral Polarization and Spectral Phase Control of Time and Energy Entangled Photons

We demonstrate a scheme to spectrally manipulate a collinear, continuous stream of time and energy entangled photons to generate beamlike, bandwidth-limited fuxes of polarization-entangled photons with nearly-degenerate wavelengths. Utilizing an ultrashort-pulse shaper to control the spectral phase and polarization of the photon pairs, we tailor the shape of the Hong-Ou-Mandel interference pattern, demonstrating the rules that govern the dependence of this interference pattern on the spectral phases of the photons. We then use the pulse shaper to generate all four polarization Bell states. The singlet state generated by this scheme forms a very robust decoherence-free subspace, extremely suitable for long distance fiber-optics based quantum communication.Comment: 5 pages, 3 figure

Crystallization of the regulatory and effector domains of the key sporulation response regulator Spo0A

The key response-regulator gene of sporulation, spo0A, has been cloned from Bacillus stearothermophilus and the encoded protein purified. The DNA-binding and phospho-acceptor domains of Spo0A have been prepared by tryptic digestion of the intact protein and subsequently crystallized in forms suitable for X-ray crystallographic studies. The DNA-binding domain has been crystallized in two forms, one of which diffracts X-rays to beyond 2.5 Angstrom spacing. The crystals of the phospho-acceptor domain diffract X-rays beyond 2.0 Angstrom spacing using synchrotron radiation

Nonlinear interactions with an ultrahigh flux of broadband entangled photons

We experimentally demonstrate sum-frequency generation (SFG) with entangled photon-pairs, generating as many as 40,000 SFG photons per second, visible even to the naked eye. The nonclassical nature of the interaction is exhibited by a linear intensity-dependence of the nonlinear process. The key element in our scheme is the generation of an ultrahigh flux of entangled photons while maintaining their nonclassical properties. This is made possible by generating the down-converted photons as broadband as possible, orders of magnitude wider than the pump. This approach is readily applicable for other nonlinear interactions, and may be applicable for various quantum-measurement tasks.Comment: 4 pages, 2 figures, Accepted to Phys. Rev. Let

New Dependencies of Hierarchies in Polynomial Optimization

We compare four key hierarchies for solving Constrained Polynomial Optimization Problems (CPOP): Sum of Squares (SOS), Sum of Diagonally Dominant Polynomials (SDSOS), Sum of Nonnegative Circuits (SONC), and the Sherali Adams (SA) hierarchies. We prove a collection of dependencies among these hierarchies both for general CPOPs and for optimization problems on the Boolean hypercube. Key results include for the general case that the SONC and SOS hierarchy are polynomially incomparable, while SDSOS is contained in SONC. A direct consequence is the non-existence of a Putinar-like Positivstellensatz for SDSOS. On the Boolean hypercube, we show as a main result that Schm\"udgen-like versions of the hierarchies SDSOS*, SONC*, and SA* are polynomially equivalent. Moreover, we show that SA* is contained in any Schm\"udgen-like hierarchy that provides a O(n) degree bound.Comment: 26 pages, 4 figure

Block Coordinate Descent for Sparse NMF

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms, such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L$_1$ norm. However, present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow and other formulations for sparse NMF have been proposed such as those based on L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets

Chiral crystals in strong-coupling lattice QCD at nonzero chemical potential

We study the effective action for strong-coupling lattice QCD with one-component staggered fermions in the case of nonzero chemical potential and zero temperature. The structure of this action suggests that at large chemical potentials its ground state is a crystalline `chiral density wave' that spontaneously breaks chiral symmetry and translation invariance. In mean-field theory, on the other hand, we find that this state is unstable. We show that lattice artifacts are partly responsible for this, and suggest that if this phase exists in QCD, then finding it in Monte-Carlo simulations would require simulating on relatively fine lattices. In particular, the baryon mass in lattice units, m_B, should be considerably smaller than its strong-coupling limit of m_B~3.Comment: 33 pages, 8 figure

Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics

We show that under variation of moduli fields $\phi$ the first law of black hole thermodynamics becomes $dM = {\kappa dA\over 8\pi} + \Omega dJ + \psi dq + \chi dp - \Sigma d\phi$, where $\Sigma$ are the scalar charges. We also show that the ADM mass is extremized at fixed $A$, $J$, $(p,q)$ when the moduli fields take the fixed value $\phi_{\rm fix}(p,q)$ which depend only on electric and magnetic charges. It follows that the least mass of any black hole with fixed conserved electric and magnetic charges is given by the mass of the double-extreme black hole with these charges. Our work allows us to interpret the previously established result that for all extreme black holes the moduli fields at the horizon take a value $\phi= \phi_{\rm fix}(p,q)$ depending only on the electric and magnetic conserved charges: $\phi_{\rm fix}(p,q)$ is such that the scalar charges $\Sigma ( \phi_{\rm fix}, (p,q))=0$.Comment: 3 pages, no figures, more detailed versio