Exponential Lower Bounds via Exponential Sums

Valiant’s famous VP vs. VNP conjecture states that the symbolic permanent polynomial does not have polynomial-size algebraic circuits. However, the best upper bound on the size of the circuits computing the permanent is exponential. Informally, VNP is an exponential sum of VP-circuits. In this paper we study whether, in general, exponential sums (of algebraic circuits) require exponential-size algebraic circuits. We show that the famous Shub-Smale τ-conjecture indeed implies such an exponential lower bound for an exponential sum. Our main tools come from parameterized complexity. Along the way, we also prove an exponential fpt (fixed-parameter tractable) lower bound for the parameterized algebraic complexity class VW⁰_{nb}[], assuming the same conjecture. VW⁰_{nb}[] can be thought of as the weighted sums of (unbounded-degree) circuits, where only ± 1 constants are cost-free. To the best of our knowledge, this is the first time the Shub-Smale τ-conjecture has been applied to prove explicit exponential lower bounds. Furthermore, we prove that when this class is fpt, then a variant of the counting hierarchy, namely the linear counting hierarchy collapses. Moreover, if a certain type of parameterized exponential sums is fpt, then integers, as well as polynomials with coefficients being definable in the linear counting hierarchy have subpolynomial τ-complexity. Finally, we characterize a related class VW[], in terms of permanents, where we consider an exponential sum of algebraic formulas instead of circuits. We show that when we sum over cycle covers that have one long cycle and all other cycles have constant length, then the resulting family of polynomials is complete for VW[] on certain types of graphs

Zwitterionic Surfactant as a Promising Non‐Cytotoxic Carrier for Nanoemulsion‐Based Vaccine Development

Motivated by the lack of noncytotoxic carriers in the current vaccine, we pursued the possibility of using a zwitterionic surfactant as a carrier to improve their delivery efficiency with antigen for a nanoemulsion‐based vaccine. We identified that a nanoemulsion formulation that consists of a specific zwitterionic surfactant can effectively mediate cellular uptake of antigen despite not having cytotoxicity as compared to a nanoemulsion that consists of a cationic surfactant. We report here the first study of a zwitterionic surfactant that consists of a positive charge in the outer layer of the polar head group and a hydrophobic tail is a promising approach for enhancing the carrier’s efficacy with no noticeable toxicity under experimental condition. However, zwitterionic surfactant that has positive charge in the outer layer with additional hydrophobicity due to the presence of aromatic ring had minimal cellular uptake and transfection efficacy.We report a nanoemulsion consists of a zwitterionic surfactant can effectively mediate cellular uptake of antigen despite not having cytotoxicity as compared to a NE consists of a cationic surfactant. ZI surfactant consists of a polar head, with positive charge in the outer layer has implications of developing next generation carrier to enhance the carrier‘s efficacy while improving tolerability for the development of NE‐based vaccine.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151273/1/slct201902737_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151273/2/slct201902737.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151273/3/slct201902737-sup-0001-misc_information.pd

Numerical Analysis of Turbulent Fluid Flow and Heat Transfer in a Rectangular Elbow

The numerical analysis of turbulent fluid flow and heat transfer through a rectangular elbow has been done by model with standard wall function. Different inlet uniform velocities of 5m/s, 10m/s, 15 m/s, 20 m/s and 25 m/s corresponding to Reynolds numbers of Re1= 4.09× 104, Re2= 8.17 × 104, Re3= 12.25× 104, Re4= 16.34× 104 and Re5 =20.43 × 104 have been considered for the numerical experimentations. The fluid considered was incompressible, Newtonian non-reacting and the flow was fully turbulent. The heat transfer analysis has been carried out by considering the fluid having at a higher temperature while the wall kept at lower temperature. A detailed study of the turbulent fluid flow shows that presence of recirculation is inevitable at every corner position or at every bend indicating presence of secondary flow incurring energy losses. The velocity distributions at different stations along the downstream path of the elbow have been plotted. The presence of this adverse pressure gradient is confirmed by the reverse velocity or the negative velocity in the vicinity of the vertical wall. In the upper corner there is a vortex extending from the upper wall of the upper limb almost touching the end point of the left wall of the vertical portion of the elbow. The heat transfer also shows the similar tendency as the fluid flow field influences the convective heat transfer process. The detail temperature distributions across any cross section basically explain the dependence of the convective heat transfer on the fluid flow field

Effect of Bottom Wall Heating on the Turbulent Fluid Flow in an Asymmetric Rectangular Diffuser: an Experimental Study

Turbulent fluid flow and heat transfer in an asymmetric diffuser are important in the context of the power plant engineering such as gas turbine, aircraft propulsion systems, hydraulic turbine equipment etc. In the present study, an experimental investigation on the forced convective heat transfer considering turbulent air flow in an asymmetric rectangular diffuser duct has been done. The experimental setup considered for the analysis consists of a diffuser at different bottom wall temperatures and inlet conditions. The air enters into the diffuser at a room temperature and flows steadily under turbulent conditions undergoing thermal boundary layer development within the diffuser. Efforts have been focused to determine the effects of bottom wall heating on the recirculation bubble strength, thermal boundary layer, velocity fields, temperature profiles etc. The distribution of the local average Nusselt number and skin friction factor in the whole flow fields have been critically examined to identify the significance of bottom wall heating effects on the overall heat transfer rates

Event-shape engineering for inclusive spectra and elliptic flow in Pb-Pb collisions at root(NN)-N-S=2.76 TeV

Peer reviewe

Production of He-4 and (4) in Pb-Pb collisions at root(NN)-N-S=2.76 TeV at the LHC

Results on the production of He-4 and (4) nuclei in Pb-Pb collisions at root(NN)-N-S = 2.76 TeV in the rapidity range vertical bar y vertical bar <1, using the ALICE detector, are presented in this paper. The rapidity densities corresponding to 0-10% central events are found to be dN/dy4(He) = (0.8 +/- 0.4 (stat) +/- 0.3 (syst)) x 10(-6) and dN/dy4 = (1.1 +/- 0.4 (stat) +/- 0.2 (syst)) x 10(-6), respectively. This is in agreement with the statistical thermal model expectation assuming the same chemical freeze-out temperature (T-chem = 156 MeV) as for light hadrons. The measured ratio of (4)/He-4 is 1.4 +/- 0.8 (stat) +/- 0.5 (syst). (C) 2018 Published by Elsevier B.V.Peer reviewe