Succinct Population Protocols for Presburger Arithmetic

International audienceIn [5], Angluin et al. proved that population protocols compute exactly the predicates definable in Presburger arithmetic (PA), the first-order theory of addition. As part of this result, they presented a procedure that translates any formula $ϕ$ of quantifier-free PA with remainder predicates (which has the same expressive power as full PA) into a population protocol with $2 O(poly(|ϕ|))$ states that computes $ϕ$. More precisely, the number of states of the protocol is exponential in both the bit length of the largest coefficient in the formula, and the number of nodes of its syntax tree. In this paper, we prove that every formula $ϕ$ of quantifier-free PA with remainder predicates is computable by a leaderless population protocol with $O(poly(|ϕ|))$ states. Our proof is based on several new constructions, which may be of independent interest. Given a formula $ϕ$ of quantifier-free PA with remainder predicates, a first construction produces a succinct protocol (with $O(|ϕ| 3)$ leaders) that computes ϕ; this completes the work initiated in [8], where we constructed such protocols for a fragment of PA. For large enough inputs, we can get rid of these leaders. If the input is not large enough, then it is small, and we design another construction producing a succinct protocol with one leader that computes $ϕ$. Our last construction gets rid of this leader for small inputs

Efficiently Constructing Convex Approximation Sets in Multiobjective Optimization Problems

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the approximation set up to a multiplicative factor in each component, a convex approximation set only requires this multiplicative approximation to be achieved by some convex combination of finitely many images of solutions in the set. This makes convex approximation sets efficiently computable for a wide range of multiobjective problems - even for many problems for which (classic) approximations sets are hard to compute. In this article, we propose a polynomial-time algorithm to compute convex approximation sets that builds upon an exact or approximate algorithm for the weighted sum scalarization and is, therefore, applicable to a large variety of multiobjective optimization problems. The provided convex approximation quality is arbitrarily close to the approximation quality of the underlying algorithm for the weighted sum scalarization. In essence, our algorithm can be interpreted as an approximate variant of the dual variant of Benson's Outer Approximation Algorithm. Thus, in contrast to existing convex approximation algorithms from the literature, information on solutions obtained during the approximation process is utilized to significantly reduce both the practical running time and the cardinality of the returned solution sets while still guaranteeing the same worst-case approximation quality. We underpin these advantages by the first comparison of all existing convex approximation algorithms on several instances of the triobjective knapsack problem and the triobjective symmetric metric traveling salesman problem

Using Scalarizations for the Approximation of Multiobjective Optimization Problems: Towards a General Theory

We study the approximation of general multiobjective optimization problems with the help of scalarizations. Existing results state that multiobjective minimization problems can be approximated well by norm-based scalarizations. However, for multiobjective maximization problems, only impossibility results are known so far. Countering this, we show that all multiobjective optimization problems can, in principle, be approximated equally well by scalarizations. In this context, we introduce a transformation theory for scalarizations that establishes the following: Suppose there exists a scalarization that yields an approximation of a certain quality for arbitrary instances of multiobjective optimization problems with a given decomposition specifying which objective functions are to be minimized / maximized. Then, for each other decomposition, our transformation yields another scalarization that yields the same approximation quality for arbitrary instances of problems with this other decomposition. In this sense, the existing results about the approximation via scalarizations for minimization problems carry over to any other objective decomposition -- in particular, to maximization problems -- when suitably adapting the employed scalarization. We further provide necessary and sufficient conditions on a scalarization such that its optimal solutions achieve a constant approximation quality. We give an upper bound on the best achievable approximation quality that applies to general scalarizations and is tight for the majority of norm-based scalarizations applied in the context of multiobjective optimization. As a consequence, none of these norm-based scalarizations can induce approximation sets for optimization problems with maximization objectives, which unifies and generalizes the existing impossibility results concerning the approximation of maximization problems

Accurate determination of elastic parameters for multi-component membranes

Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line tension and the bending moduli, are crucially involved in the kinetics and the asymptotic behavior of phase separation. In this Letter we present a combined analytical and experimental approach to determine the properties of phase-separated vesicle systems. First we develop an analytical model for the vesicle shape of weakly budded biphasic vesicles. Subsequently experimental data on vesicle shape and membrane fluctuations are taken and compared to the model. The combined approach allows for a reproducible and reliable determination of the physical parameters of complex vesicle systems. The parameters obtained set limits for the size and stability of nanodomains in the plasma membrane of living cells.Comment: (*) authors contributed equally, 6 pages, 3 figures, 1 table; added insets to figure

Rapid inoculation of single bacteria into parallel picoliter fermentation chambers

Probst C, Grünberger A, Braun N, et al. Rapid inoculation of single bacteria into parallel picoliter fermentation chambers. Analytical methods. 2015;7(1):91-98.Microfluidic single-cell cultivation devices have been successfully utilized in a variety of biological research fields. One major obstacle to the successful implementation of high throughput single-cell cultivation technology is the requirement for a simple, fast and reliable cell inoculation procedure. In the present report, an air-bubble-based cell loading methodology is described and validated for inoculating single bacteria into multiple picoliter sized growth chambers arranged in a highly parallel manner. It is shown that the application of the injected air bubble can serve as a reproducible mechanism to modify laminar flow conditions. In this way, convective flow was temporarily induced in more than 1000 cultivation chambers simultaneously, which under normal conditions operate exclusively under diffusive mass transport. Within an inoculation time of 100 s, Corynebacterium glutamicum cells were inoculated by convection at minimal stress level and single bacteria remain successfully trapped by cell-wall interactions. The procedure is easy, fast, gentle and requires only minimal fluidic control and equipment. The technique is well suited for microbial cell loading into commonly used microfluidic growth sites arranged in parallel intended for high throughput single-cell analysis

Hybrid simulations of lateral diffusion in fluctuating membranes

In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

Spatiotemporally restricted arenavirus replication induces immune surveillance and type I interferon-dependent tumour regression

Immune-mediated effector molecules can limit cancer growth, but lack of sustained immune activation in the tumour microenvironment restricts antitumour immunity. New therapeutic approaches that induce a strong and prolonged immune activation would represent a major immunotherapeutic advance. Here we show that the arenaviruses lymphocytic choriomeningitis virus (LCMV) and the clinically used Junin virus vaccine (Candid#1) preferentially replicate in tumour cells in a variety of murine and human cancer models. Viral replication leads to prolonged local immune activation, rapid regression of localized and metastatic cancers, and long-term disease control. Mechanistically, LCMV induces antitumour immunity, which depends on the recruitment of interferon-producing Ly6C+ monocytes and additionally enhances tumour-specific CD8+ T cells. In comparison with other clinically evaluated oncolytic viruses and to PD-1 blockade, LCMV treatment shows promising antitumoural benefits. In conclusion, therapeutically administered arenavirus replicates in cancer cells and induces tumour regression by enhancing local immune responses

CSPG4:A Target for Selective Delivery of Human Cytolytic Fusion Proteins and TRAIL

Chondroitin-sulfate proteoglycan 4 (CSPG4) is a transmembrane glycoprotein overexpressed on malignant cells in several cancer types with only limited expression on normal cells. CSPG4 is implicated in several signaling pathways believed to drive cancer progression, particularly proliferation, motility and metastatic spread. Expression may serve as a prognostic marker for survival and risk of relapse in treatment-resistant malignancies including melanoma, triple negative breast cancer, rhabdomyosarcoma and acute lymphoblastic leukemia. This tumor-associated overexpression of CSPG4 points towards a highly promising therapeutic target for antibody-guided cancer therapy. Monoclonal αCSPG4 antibodies have been shown to inhibit cancer progression by blocking ligand access to the CSPG4 extracellular binding sites. Moreover, CSPG4-directed antibody conjugates have been shown to be selectively internalized by CSPG4-expressing cancer cells via endocytosis. CSPG4-directed immunotherapy may be approached in several ways, including: (1) antibody-based fusion proteins for the selective delivery of a pro-apoptotic factors such as tumor necrosis factor-related apoptosis-inducing ligand to agonistic death receptors 4 and 5 on the cell surface; and (2) CSPG4-specific immunotoxins which bind selectively to diseased cells expressing CSPG4, are internalized by them and induce arrest of biosynthesis, closely followed by initiation of apoptotic signaling. Here we review various methods of exploiting tumor-associated CSPG4 expression to improve targeted cancer therapy