Monotone Proofs of the Pigeon Hole Principle

Lecture Notes in Computer Science. Geneva, Switzerland, July 9-15

Bounded-depth Frege complexity of Tseitin formulas for all graphs

We prove that there is a constant K such that Tseitin formulas for a connected graph G requires proofs of size 2tw(G)javax.xml.bind.JAXBElement@531a834b in depth-d Frege systems for [Formula presented], where tw(G) is the treewidth of G. This extends Håstad's recent lower bound from grid graphs to any graph. Furthermore, we prove tightness of our bound up to a multiplicative constant in the top exponent. Namely, we show that if a Tseitin formula for a graph G has size s, then for all large enough d, it has a depth-d Frege proof of size 2tw(G)javax.xml.bind.JAXBElement@25a4b51fpoly(s). Through this result we settle the question posed by M. Alekhnovich and A. Razborov of showing that the class of Tseitin formulas is quasi-automatizable for resolution

On the Algebraic Proof Complexity of Tensor Isomorphism

The Tensor Isomorphism problem (TI) has recently emerged as having connections to multiple areas of research within complexity and beyond, but the current best upper bound is essentially the brute force algorithm. Being an algebraic problem, TI (or rather, proving that two tensors are non-isomorphic) lends itself very naturally to algebraic and semi-algebraic proof systems, such as the Polynomial Calculus (PC) and Sum of Squares (SoS). For its combinatorial cousin Graph Isomorphism, essentially optimal lower bounds are known for approaches based on PC and SoS (Berkholz & Grohe, SODA \u2717). Our main results are an ?(n) lower bound on PC degree or SoS degree for Tensor Isomorphism, and a nontrivial upper bound for testing isomorphism of tensors of bounded rank. We also show that PC cannot perform basic linear algebra in sub-linear degree, such as comparing the rank of two matrices (which is essentially the same as 2-TI), or deriving BA = I from AB = I. As linear algebra is a key tool for understanding tensors, we introduce a strictly stronger proof system, PC+Inv, which allows as derivation rules all substitution instances of the implication AB = I ? BA = I. We conjecture that even PC+Inv cannot solve TI in polynomial time either, but leave open getting lower bounds on PC+Inv for any system of equations, let alone those for TI. We also highlight many other open questions about proof complexity approaches to TI

The effect of medium composition on interleukin-2 production by murine EL-4 thymoma cells

Due to the role of interleukin-2 (IL-2) in the mediation of immune response, this cytokine has been used in the treatment of some types of cancer and infectious diseases. However, relatively high levels of this cytokine are required to achieve significant activity. The aim of this work was to study a culture medium composition designed to increase the production of IL-2 by suspended murine EL-4 cells. The cultivations were carried out aiming at producing IL-2 in stirred bioreactors. The effects of concentration of glutamine, phorbol-12-myristate-13-acetate (PMA), concanavalin A (Con A), Pluronic F68, and fetal calf serum (FCS) on cell viability and IL-2 production were evaluated. PMA alone was more efficient in IL-2 production than it was in association with Con A. The maximum IL-2 production was around 162 ng/mL with 856 ng/mL PMA and 1.45% (v/v) FCS.16517

Analysis of acoustic climate on board public transport

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Dissipative hydrodynamics of relativistic shock waves in a Quark Gluon Plasma: comparing and benchmarking alternate numerical methods

This paper presents numerical cross-comparisons and benchmark results for two different kinetic numerical methods, capable of describing relativistic dissipative fluid dynamics in a wide range of kinematic regimes, typical of relevant physics applications, such as transport phenomena in quark-gluon plasmas. We refer to relativistic lattice Boltzmann versus Montecarlo Test-Particle methods. Lacking any realistic option for accurate validation vis-a-vis experimental data, we check the consistency of our results against established simulation packages available in the literature. We successfully cross-compare the results of the two aforementioned numerical approaches for momentum integrated quantities like the hydrostatic and dynamical pressure profiles, the collective flow and the heat flux. These results corroborate the confidence on the robustness and correctness of these computational methods and on the accurate calibration of their numerical parameters with respect to the physical transport coefficients. Our numerical results are made available as supplemental material, with the aim of establishing a reference benchmark for other numerical approaches

The application of GIS to air quality analysis in Enna City (Italy)

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