@unpublished{3742, abstract = {Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes. Finding these models requires us to solve an inverse problem: given experimentally measured expectation values, what are the parameters of the underlying Hamiltonian? This problem sits at the intersection of statistical physics and machine learning, and we suggest that more efficient solutions are possible by merging ideas from the two fields. We use a combination of recent coordinate descent algorithms with an adaptation of the histogram Monte Carlo method, and implement these techniques to take advantage of the sparseness found in data on real neurons. The resulting algorithm learns the parameters of an Ising model describing a network of forty neurons within a few minutes. This opens the possibility of analyzing much larger data sets now emerging, and thus testing hypotheses about the collective behaviors of these networks.}, author = {Broderick,Tamara and Dudik,Miroslav and Gasper Tkacik and Schapire,Robert E and Bialek, William S}, booktitle = {ArXiv}, publisher = {ArXiv}, title = {{Faster solutions of the inverse pairwise Ising problem}}, volume = {q-bio.QM}, year = {2007}, } @article{4234, abstract = {We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two sources of multiplicative noise. The stationary probability distributions have two characteristic power-law scales. Numerical simulations show that noise suppresses the explosion of the growth rate which occurs in the deterministic counterpart. Instead, in different parameter regimes populations will grow with "anomalous" stochastic rates and (i) stabilise at "random carrying capacities", or (ii) go extinct in random times. Using logistic fits to reconstruct the simulated data, we find that even highly significant estimations do not recover or reflect information about the deterministic part of the process. Therefore, the logistic interpretation is not biologically meaningful. These results have implications for distinct model-aided calculations in biological situations because these kinds of estimations could lead to spurious conclusions. (c) 2006 Elsevier B.V. All rights reserved.}, author = {de Vladar, Harold and Pen, I.}, journal = {Physica A}, pages = {477 -- 485}, publisher = {Elsevier}, title = {{Determinism, noise, and spurious estimations in a generalised model of population growth}}, doi = {10.1016/j.physa.2006.06.025}, volume = {373}, year = {2007}, } @inproceedings{2091, abstract = {We present a novel multi-scale representation and acquisition method for the animation of high-resolution facial geometry and wrinkles. We first acquire a static scan of the face including reflectance data at the highest possible quality. We then augment a traditional marker-based facial motion-capture system by two synchronized video cameras to track expression wrinkles. The resulting model consists of high-resolution geometry, motion-capture data, and expression wrinkles in 2D parametric form. This combination represents the facial shape and its salient features at multiple scales. During motion synthesis the motion-capture data deforms the high-resolution geometry using a linear shell-based mesh-deformation method. The wrinkle geometry is added to the facial base mesh using nonlinear energy optimization. We present the results of our approach for performance replay as well as for wrinkle editing. }, author = {Bernd Bickel and Botsch, Mario and Angst, Roland and Matusik, Wojciech and Otaduy, Miguel A and Pfister, Hanspeter and Groß, Markus S}, publisher = {ACM}, title = {{Multi scale capture of facial geometry and motion}}, doi = {doi:10.1145/1275808.1276419}, year = {2007}, } @article{2093, abstract = {We present a novel multi-scale representation and acquisition method for the animation of high-resolution facial geometry and wrinkles. We first acquire a static scan of the face including reflectance data at the highest possible quality. We then augment a traditional marker-based facial motion-capture system by two synchronized video cameras to track expression wrinkles. The resulting model consists of high-resolution geometry, motion-capture data, and expression wrinkles in 2D parametric form. This combination represents the facial shape and its salient features at multiple scales. During motion synthesis the motion-capture data deforms the high-resolution geometry using a linear shell-based mesh-deformation method. The wrinkle geometry is added to the facial base mesh using nonlinear energy optimization. We present the results of our approach for performance replay as well as for wrinkle editing. }, author = {Bernd Bickel and Botsch, Mario and Angst, Roland and Matusik, Wojciech and Otaduy, Miguel A and Pfister, Hanspeter and Groß, Markus S}, journal = {ACM Transactions on Graphics}, number = {3}, publisher = {ACM}, title = {{Multi scale capture of facial geometry and motion}}, doi = {10.1145/1276377.1276419}, volume = {26}, year = {2007}, } @article{2118, abstract = {We extend to infinite dimensions an explicit formula of Chill, Fašangová, Metafune, and Pallara for the optimal angle of analyticity of analytic Ornstein-Uhlenbeck semigroups. The main ingredient is an abstract representation of the Ornstein-Uhlenbeck operator in divergence form. }, author = {Jan Maas and van Neerven, Jan M}, journal = {Archiv der Mathematik}, number = {3}, pages = {226 -- 236}, publisher = {Birkhäuser}, title = {{On analytic Ornstein-Uhlenbeck semigroups in infinite dimensions}}, doi = {10.1007/s00013-007-2082-x}, volume = {89}, year = {2007}, } @article{221, author = {De La Bretèche, Régis and Browning, Timothy D}, journal = {Michigan Mathematical Journal}, number = {1}, pages = {51 -- 80}, publisher = {Project Euclid}, title = {{On Manin's conjecture for singular del Pezzo surfaces of degree four, I}}, doi = {10.1307/mmj/1177681985}, volume = {55}, year = {2007}, } @article{222, abstract = {Acknowledgements. The authors are grateful to Ulrich Derenthal and Brendan Hassett for several useful conversations relating to universal torsors for singular del Pezzo surfaces. Special thanks are due to Roger Heath–Brown whose ideas led us to the proof of Lemma 6. The paper was finalised while the first author was at the École Normale Supérieure, and the second author was at Oxford University supported by EPSRC grant number GR/R93155/01. The hospitality and financial support of these institutions is gratefully acknowledged. Finally, the authors would like to thank the anonymous referee for his careful reading of the manuscript and numerous useful suggestions.}, author = {de la Bretèche, Régis and Timothy Browning}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society}, number = {3}, pages = {579 -- 605}, publisher = {Unknown}, title = {{On Manin's conjecture for singular del Pezzo surfaces of degree four, II}}, doi = {10.1017/S0305004107000205}, volume = {143}, year = {2007}, } @article{223, abstract = {Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B → ∞. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.}, author = {Timothy Browning}, journal = {Monatshefte fur Mathematik}, number = {1}, pages = {13 -- 38}, publisher = {Springer}, title = {{Density of integer solutions to diagonal quadratic forms}}, doi = {10.1007/s00605-007-0457-5}, volume = {152}, year = {2007}, } @article{2367, abstract = {It was recently shown by Hansen that the Wigner-Yanase entropy is, for general states of quantum systems, not subadditive with respect to decomposition into two subsystems, although this property is known to hold for pure states. We investigate the question whether the weaker property of subadditivity for pure states with respect to decomposition into more than two subsystems holds. This property would have interesting applications in quantum chemistry. We show, however, that it does not hold in general, and provide a counterexample.}, author = {Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {3}, pages = {285 -- 288}, publisher = {Springer}, title = {{On the failure of subadditivity of the Wigner-Yanase entropy}}, doi = {10.1007/s11005-007-0159-x}, volume = {80}, year = {2007}, } @article{2370, abstract = {After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α0.}, author = {Lieb, Élliott H and Robert Seiringer and Yngvason, Jakob}, journal = {Reports on Mathematical Physics}, number = {3}, pages = {389 -- 399}, publisher = {Elsevier}, title = {{Bose-Einstein condensation and spontaneous symmetry breaking}}, doi = {10.1016/S0034-4877(07)80074-7}, volume = {59}, year = {2007}, } @article{2371, abstract = {We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zα = 2/π.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer}, journal = {Communications in Mathematical Physics}, number = {2}, pages = {479 -- 489}, publisher = {Springer}, title = {{Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value}}, doi = {10.1007/s00220-007-0307-2}, volume = {275}, year = {2007}, } @article{2372, abstract = {The increasing interest in the Müller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock (HF) functional, but with a modified exchange term in which the square of the density matrix γ(x, x′) is replaced by the square of γ1 2 (x, x′). After an extensive introductory discussion of density-matrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing γ 's have unique densities ρ(r), which is a physically desirable property often absent in HF theory. We show that minimizers exist if N≤Z, and derive various properties of the minimal energy and the corresponding minimizers. We also give a precise statement about the equation for the orbitals of γ, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer and Siedentop, Heinz K}, journal = {Physical Review A - Atomic, Molecular, and Optical Physics}, number = {5}, publisher = {American Physical Society}, title = {{Müller's exchange-correlation energy in density-matrix-functional theory}}, doi = {10.1103/PhysRevA.76.052517}, volume = {76}, year = {2007}, } @article{2373, abstract = {For the BCS equation with local two-body interaction λV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as γ"0. We derive necessary and sufficient conditions onV(x) for the existence of a nontrivial solution for all values of γ>0.}, author = {Frank, Rupert L and Hainzl, Christian and Naboko, Serguei N and Robert Seiringer}, journal = {Journal of Geometric Analysis}, number = {4}, pages = {559 -- 567}, publisher = {Springer}, title = {{The critical temperature for the BCS equation at weak coupling}}, doi = {10.1007/BF02937429}, volume = {17}, year = {2007}, } @article{2375, abstract = {We give a Cwikel-Lieb-Rozenblum type bound on the number of bound states of Schrödinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.}, author = {Frank, Rupert L and Lieb, Élliott H and Robert Seiringer}, journal = {Letters in Mathematical Physics}, number = {2-3}, pages = {107 -- 116}, publisher = {Springer}, title = {{Number of bound states of Schrödinger operators with matrix-valued potentials}}, doi = {10.1007/s11005-007-0211-x}, volume = {82}, year = {2007}, } @inbook{2705, author = {László Erdös}, booktitle = {Spectral Theory and Mathematical Physics: a Festschrift in Honor of Barry Simon's 60th Birthday }, editor = {Gesztesy, Fritz and Deift, Percy and Galvez, Percy and Perry, Peter and Schlag, Wilhelm}, pages = {401 -- 428}, publisher = {American Mathematical Society}, title = {{Recent developments in quantum mechanics with magnetic fields}}, volume = {76}, year = {2007}, } @article{11116, abstract = {The metazoan nuclear envelope (NE) breaks down and re-forms during each cell cycle. Nuclear pore complexes (NPCs), which allow nucleocytoplasmic transport during interphase, assemble into the re-forming NE at the end of mitosis. Using in vitro NE assembly, we show that the vertebrate homologue of MEL-28 (maternal effect lethal), a recently discovered NE component in Caenorhabditis elegans, functions in postmitotic NPC assembly. MEL-28 interacts with the Nup107–160 complex (Nup for nucleoporin), an important building block of the NPC, and is essential for the recruitment of the Nup107–160 complex to chromatin. We suggest that MEL-28 acts as a seeding point for NPC assembly.}, author = {Franz, Cerstin and Walczak, Rudolf and Yavuz, Sevil and Santarella, Rachel and Gentzel, Marc and Askjaer, Peter and Galy, Vincent and HETZER, Martin W and Mattaj, Iain W and Antonin, Wolfram}, issn = {1469-3178}, journal = {EMBO reports}, keywords = {Genetics, Molecular Biology, Biochemistry}, number = {2}, pages = {165--172}, publisher = {EMBO}, title = {{MEL‐28/ELYS is required for the recruitment of nucleoporins to chromatin and postmitotic nuclear pore complex assembly}}, doi = {10.1038/sj.embor.7400889}, volume = {8}, year = {2007}, } @article{1461, abstract = {This note proves combinatorially that the intersection pairing on the middle-dimensional compactly supported cohomology of a toric hyperkähler variety is always definite, providing a large number of non-trivial L 2 harmonic forms for toric hyperkähler metrics on these varieties. This is motivated by a result of Hitchin about the definiteness of the pairing of L 2 harmonic forms on complete hyperkähler manifolds of linear growth.}, author = {Tamas Hausel and Swartz, Edward}, journal = {Proceedings of the American Mathematical Society}, number = {8}, pages = {2403 -- 2409}, publisher = {American Mathematical Society}, title = {{Intersection forms of toric hyperkähler varieties}}, doi = {10.1090/S0002-9939-06-08248-7}, volume = {134}, year = {2006}, } @article{1462, abstract = {A Fourier transform technique is introduced for counting the number of solutions of holomorphic moment map equations over a finite field. This technique in turn gives information on Betti numbers of holomorphic symplectic quotients. As a consequence, simple unified proofs are obtained for formulas of Poincaré polynomials of toric hyperkähler varieties (recovering results of Bielawski-Dancer and Hausel-Sturmfels), Poincaré polynomials of Hubert schemes of points and twisted Atiyah-Drinfeld-Hitchin-Manin (ADHM) spaces of instantons on ℂ2 (recovering results of Nakajima-Yoshioka), and Poincaré polynomials of all Nakajima quiver varieties. As an application, a proof of a conjecture of Kac on the number of absolutely indecomposable representations of a quiver is announced.}, author = {Tamas Hausel}, journal = {PNAS}, number = {16}, pages = {6120 -- 6124}, publisher = {National Academy of Sciences}, title = {{Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform}}, doi = {10.1073/pnas.0601337103}, volume = {103}, year = {2006}, } @unpublished{573, abstract = {Mitchison and Jozsa recently suggested that the "chained-Zeno" counterfactual computation protocol recently proposed by Hosten et al. is counterfactual for only one output of the computer. This claim was based on the existing abstract algebraic definition of counterfactual computation, and indeed according to this definition, their argument is correct. However, a more general definition (physically adequate) for counterfactual computation is implicitly assumed by Hosten et. al. Here we explain in detail why the protocol is counterfactual and how the "history tracking" method of the existing description inadequately represents the physics underlying the protocol. Consequently, we propose a modified definition of counterfactual computation. Finally, we comment on one of the most interesting aspects of the error-correcting protocol. }, author = {Hosten, Onur and Rakher, Matthew and Barreiro, Julio and Peters, Nicholas and Kwiat, Paul}, pages = {12}, publisher = {ArXiv}, title = {{Counterfactual computation revisited}}, year = {2006}, } @unpublished{574, abstract = {Vaidman, in a recent article adopts the method of 'quantum weak measurements in pre- and postselected ensembles' to ascertain whether or not the chained-Zeno counterfactual computation scheme proposed by Hosten et al. is counterfactual; which has been the topic of a debate on the definition of counterfactuality. We disagree with his conclusion, which brings up some interesting aspects of quantum weak measurements and some concerns about the way they are interpreted. }, author = {Hosten, Onur and Kwiat, Paul}, pages = {2}, publisher = {ArXiv}, title = {{Weak measurements and counterfactual computation}}, year = {2006}, }