TY - JOUR AB - Autism spectrum disorders are a genetically heterogeneous constellation of syndromes characterized by impairments in reciprocal social interaction. Available somatic treatments have limited efficacy. We have identified inactivating mutations in the gene BCKDK (Branched Chain Ketoacid Dehydrogenase Kinase) in consanguineous families with autism, epilepsy, and intellectual disability. The encoded protein is responsible for phosphorylation-mediated inactivation of the E1α subunit of branched-chain ketoacid dehydrogenase (BCKDH). Patients with homozygous BCKDK mutations display reductions in BCKDK messenger RNA and protein, E1α phosphorylation, and plasma branched-chain amino acids. Bckdk knockout mice show abnormal brain amino acid profiles and neurobehavioral deficits that respond to dietary supplementation. Thus, autism presenting with intellectual disability and epilepsy caused by BCKDK mutations represents a potentially treatable syndrome. AU - Gaia Novarino AU - El-Fishawy, Paul AU - Kayserili, Hülya AU - Meguid, Nagwa A AU - Scott, Eric M AU - Schroth, Jana AU - Silhavy, Jennifer L AU - Kara, Majdi AU - Khalil, Rehab O AU - Ben-Omran, Tawfeg I AU - Ercan-Sencicek, Adife G AU - Hashish, Adel F AU - Sanders, Stephan J AU - Gupta, Abha R AU - Hashem, Hebatalla S AU - Matern, Dietrich AU - Gabriel, Stacey B AU - Sweetman, Lawrence AU - Rahimi, Yasmeen AU - Harris, Robert A AU - State, Matthew W AU - Gleeson, Joseph G ID - 2314 IS - 6105 JF - Science TI - Mutations in BCKD-kinase lead to a potentially treatable form of autism with epilepsy VL - 338 ER - TY - JOUR AB - We show that bosons interacting via pair potentials with negative scattering length form bound states for a suitable number of particles. In other words, the absence of many-particle bound states of any kind implies the non-negativity of the scattering length of the interaction potential. AU - Seiringer, Robert ID - 2318 IS - 3 JF - Journal of Spectral Theory TI - Absence of bound states implies non-negativity of the scattering length VL - 2 ER - TY - CONF AB - We present a summary of our recent rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. AU - Frank, Rupert L AU - Hainzl, Christian AU - Robert Seiringer AU - Solovej, Jan P ID - 2317 TI - Microscopic derivation of the Ginzburg-Landau model ER - TY - CONF AB - We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of binding in the case of large Coulomb repulsion and the corresponding binding-unbinding transition. We also consider the Pekar-Tomasevich approximation to the ground state energy and we study radial symmetry of the ground state density. AU - Frank, Rupert L AU - Lieb, Élliott H AU - Robert Seiringer AU - Thomas, Lawrence E ID - 2316 TI - Ground state properties of multi-polaron systems ER - TY - JOUR AB - The Manin conjecture is established for Châtelet surfaces over Q aris-ing as minimal proper smooth models of the surface Y 2 + Z 2 = f(X) in A 3 Q, where f ∈ Z[X] is a totally reducible polynomial of degree 3 without repeated roots. These surfaces do not satisfy weak approximation. AU - de la Bretèche, Régis AU - Timothy Browning AU - Peyre, Emmanuel ID - 237 IS - 1 JF - Annals of Mathematics TI - On Manin's conjecture for a family of Châtelet surfaces VL - 175 ER - TY - JOUR AB - For given positive integers a, b, q we investigate the density of solutions (x, y) ∈ Z2 to congruences ax + by2 ≡ 0 mod q. AU - Baier, Stephan AU - Timothy Browning ID - 238 IS - 2 JF - Functiones et Approximatio, Commentarii Mathematici TI - Inhomogeneous quadratic congruences VL - 47 ER - TY - CHAP AB - Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures. AU - Robert Seiringer ED - Rivasseau, Vincent ED - Robert Seiringer ED - Solovej, Jan P ED - Spencer, Thomas ID - 2399 T2 - Quantum Many Body Systems TI - Cold quantum gases and bose einstein condensation VL - 2051 ER - TY - JOUR AB - We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δ μ/T) ≤ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal.17, 559-567 (2007)10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys.281, 349-367 (2008)10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B77, 184517-110 435 (2008)]10.1103/PhysRevB.77.184517. For cosh (δ μ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit. AU - Freiji, Abraham AU - Hainzl, Christian AU - Robert Seiringer ID - 2394 IS - 1 JF - Journal of Mathematical Physics TI - The gap equation for spin-polarized fermions VL - 53 ER - TY - JOUR AB - We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof. AU - Frank, Rupert L AU - Hainzl, Christian AU - Robert Seiringer AU - Solovej, Jan P ID - 2395 IS - 3 JF - Journal of the American Mathematical Society TI - Microscopic derivation of Ginzburg-Landau theory VL - 25 ER - TY - JOUR AB - A positive temperature analogue of the scattering length of a potential V can be defined via integrating the difference of the heat kernels of -Δ and, with Δ the Laplacian. An upper bound on this quantity is a crucial input in the derivation of a bound on the critical temperature of a dilute Bose gas (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009). In (Seiringer and Ueltschi in Phys Rev B 80:014502, 2009), a bound was given in the case of finite range potentials and sufficiently low temperature. In this paper, we improve the bound and extend it to potentials of infinite range. AU - Landon, Benjamin AU - Robert Seiringer ID - 2396 IS - 3 JF - Letters in Mathematical Physics TI - The scattering length at positive temperature VL - 100 ER - TY - GEN AB - We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time. AU - Jakšić, Vojkan AU - Ogata, Yoshiko AU - Pillet, Claude A AU - Robert Seiringer ID - 2398 IS - 6 T2 - Reviews in Mathematical Physics TI - Quantum hypothesis testing and non-equilibrium statistical mechanics VL - 24 ER - TY - JOUR AB - We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs. AU - Hainzl, Christian AU - Robert Seiringer ID - 2397 IS - 2 JF - Letters in Mathematical Physics TI - Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs VL - 100 ER - TY - JOUR AB - We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior. AU - Timothy Browning AU - Valckenborgh, K Van ID - 240 IS - 2 JF - Experimental Mathematics TI - Sums of three squareful numbers VL - 21 ER - TY - JOUR AB - If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2. AU - Frank, Rupert L AU - Lieb, Élliott H AU - Robert Seiringer ID - 2400 IS - 2 JF - Communications in Mathematical Physics TI - Binding of polarons and atoms at threshold VL - 313 ER - TY - JOUR AB - We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose-Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval. AU - Robert Seiringer AU - Yngvason, Jakob AU - Zagrebnov, Valentin A ID - 2403 IS - 11 JF - Journal of Statistical Mechanics Theory and Experiment TI - Disordered Bose-Einstein condensates with interaction in one dimension VL - 2012 ER - TY - JOUR AB - We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power. AU - Frank, Rupert L AU - Robert Seiringer ID - 2402 IS - 9 JF - Journal of Mathematical Physics TI - Lieb-Thirring inequality for a model of particles with point interactions VL - 53 ER - TY - JOUR AB - We find further implications of the BMV conjecture, which states that for hermitian matrices B≥0 and A, the function λ {mapping} Tr exp(A - λB) is the Laplace transform of a positive measure supported on [0,∞]. AU - Lieb, Élliott H AU - Robert Seiringer ID - 2401 IS - 1 JF - Journal of Statistical Physics TI - Further implications of the Bessis-Moussa-Villani conjecture VL - 149 ER - TY - JOUR AB - The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses. AU - Ebersberger, Ingo AU - De Matos Simoes, Ricardo AU - Kupczok, Anne AU - Gube, Matthias AU - Kothe, Erika AU - Voigt, Kerstin AU - Von Haeseler, Arndt ID - 2411 IS - 5 JF - Molecular Biology and Evolution TI - A consistent phylogenetic backbone for the fungi VL - 29 ER - TY - JOUR AB - The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces over ℚ. AU - de la Bretèche, Régis AU - Timothy Browning ID - 241 IS - 2 JF - Israel Journal of Mathematics TI - Binary forms as sums of two squares and Châtelet surfaces VL - 191 ER - TY - JOUR AB - We investigate the first and second moments of shifted convolutions of the generalized divisor function d 3(n). AU - Baier, Stephan AU - Timothy Browning AU - Marasingha, Gihan AU - Zhao, Liangyi ID - 242 IS - 3 JF - Proceedings of the Edinburgh Mathematical Society TI - Averages of shifted convolutions of d3 (n) VL - 55 ER -