Pseudorandom Generators for Width-3 Branching Programs

We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom generators with seed length $\tilde{O}(\log(n) \cdot \mathrm{poly}(1/\epsilon))$. This is the first improvement for pseudorandom generators fooling width $3$ ROBPs since the work of Nisan [Combinatorica, 1992]. Our constructions are based on the `iterated milder restrictions' approach of Gopalan et al. [FOCS, 2012] (which further extends the Ajtai-Wigderson framework [FOCS, 1985]), combined with the INW-generator [STOC, 1994] at the last step (as analyzed by Braverman et al. [SICOMP, 2014]). For the unordered case, we combine iterated milder restrictions with the generator of Chattopadhyay et al. [CCC, 2018]. Two conceptual ideas that play an important role in our analysis are: (1) A relabeling technique allowing us to analyze a relabeled version of the given branching program, which turns out to be much easier. (2) Treating the number of colliding layers in a branching program as a progress measure and showing that it reduces significantly under pseudorandom restrictions. In addition, we achieve nearly optimal seed-length $\tilde{O}(\log(n/\epsilon))$ for the classes of: (1) read-once polynomials on $n$ variables, (2) locally-monotone ROBPs of length $n$ and width $3$ (generalizing read-once CNFs and DNFs), and (3) constant-width ROBPs of length $n$ having a layer of width $2$ in every consecutive $\mathrm{poly}\log(n)$ layers.Comment: 51 page

An epep collider based on proton-driven plasma wakefield acceleration

Recent simulations have shown that a high-energy proton bunch can excite strong plasma wakefields and accelerate a bunch of electrons to the energy frontier in a single stage of acceleration. This scheme could lead to a future $ep$ collider using the LHC for the proton beam and a compact electron accelerator of length 170 m, producing electrons of energy up to 100 GeV. The parameters of such a collider are discussed as well as conceptual layouts within the CERN accelerator complex. The physics of plasma wakefield acceleration will also be introduced, with the AWAKE experiment, a proof of principle demonstration of proton-driven plasma wakefield acceleration, briefly reviewed, as well as the physics possibilities of such an $ep$ collider.Comment: 6 pages, 2 figures, to appear in the proceedings of the DIS 2014 Workshop, 28 April - 2 May, Warsaw, Polan

Collider design issues based on proton-driven plasma wakefield acceleration

Recent simulations have shown that a high-energy proton bunch can excite strong plasma wakefields and accelerate a bunch of electrons to the energy frontier in a single stage of acceleration. It therefore paves the way towards a compact future collider design using the proton beams from existing high-energy proton machines, e.g. Tevatron or the LHC. This paper addresses some key issues in designing a compact electron-positron linear collider and an electron-proton collider based on existing CERN accelerator infrastructure

Ground state of a double-exchange system containing impurities: bounds of ferromagnetism

We study the boundary between ferromagnetic and non-ferromagnetic ground state of a double-exchange system with quenched disorder for arbitrary relation between Hund exchange coupling and electron band width. The boundary is found both from the solution of the Dynamical Mean Field Approximation equations and from the comparison of the energies of the saturated ferromagnetic and paramagnetic states. Both methods give very similar results. To explain the disappearance of ferromagnetism in part of the parameter space we derive from the double-exchange Hamiltonian with classical localized spins in the limit of large but finite Hund exchange coupling the $t-J$ model (with classical localized spins).Comment: 5 pages, 8 eps figures, latex; minor typos correcte

Dynamical Mean Field Theory of Double Perovskite Ferrimagnets

The dynamical mean field method is used to analyze the magnetic transition temperature and optical conductivity of a model for the ferrimagnetic double perovskites such as $Sr_2FeMoO_6$. The calculated transition temperatures and optical conductivities are found to depend sensitively on the band structure. For parameters consistent with local spin density approximation band calculations, the computed transition temperatures are lower than observed, and in particular decrease dramatically as band filling is increased, in contradiction to experiment. Band parameters which would increase the transition temperature are identified.Comment: Supercedes cond-mat/000628 (PRB64 024424/1-4 (2001

Swimming Efficiency of Bacterium Escherichia Coli

We use in vivo measurements of swimming bacteria in an optical trap to determine fundamental properties of bacterial propulsion. In particular, we determine the propulsion matrix, which relates the angular velocity of the flagellum to the torques and forces propelling the bacterium. From the propulsion matrix dynamical properties such as forces, torques, swimming speed and power can be obtained from measurements of the angular velocity of the motor. We find significant heterogeneities among different individuals even though all bacteria started from a single colony. The propulsive efficiency, defined as the ratio of the propulsive power output to the rotary power input provided by the motors, is found to be 0.2%.Comment: 6 page

Structural domain and spin ordering induced glassy magnetic phase in single layered manganite Pr0.22_{0.22}Sr1.78_{1.78}MnO4_4

The single layered manganite Pr$_{0.22}$Sr$_{1.78}$MnO$_4$ undergoes structural transition from high temperature tetragonal phase to low temperature orthorhombic phase below room temperature. The orthorhombic phase was reported to have two structural variants with slightly different lattice parameters and Mn-3$d$ levels show orbital ordering within both the variants, albeit having mutually perpendicular ordering axis. In addition to orbital ordering, the orthorhombic variants also order antiferromagnetically with different N\'eel temperatures. Our magnetic investigation on the polycrystalline sample of Pr$_{0.22}$Sr$_{1.78}$MnO$_4$ shows large thermal hysteresis indicating the first order nature of the tetragonal to orthorhombic transition. We observe magnetic memory, large relaxation, frequency dependent ac susceptbility and aging effects at low temperature, which indicate spin glass like magnetic ground state in the sample. The glassy magnetic state presumably arises from the interfacial frustration of orthorhombic domains with orbital and spin orderings playing crucial role toward the competing magnetic interactions.Comment: 6 pages, 4 figures, Accepted in Europhysics Letter

The LHC (CMS) Discovery Potential for Models with Effective Supersymmetry and Nonuniversal Gaugino Masses

We investigate squark and gluino pair production at LHC (CMS) with subsequent decays into quarks, leptons and LSP in models with effective supersymmetry where third generation of squarks is relatively light while the first two generations of squarks are heavy. We consider the general case of nonuniversal gaugino masses. Visibility of signal by an excess over SM background in (n \geq 2)jets + (m \geq 0)leptons + E^{miss}_T events depends rather strongly on the relation between LSP, second neutralino, gluino and squark masses and it decreases with the increase of LSP mass. We find that for relatively heavy gluino it is very difficult to detect SUSY signal even for light 3^{rd} generation squarks (m_{\tilde q_3}\le 1 TeV) if the LSP mass is closed to the 3^{rd} generation squark mass.Comment: 1 latex (35 pages), 4 eps (figures) file