Domain walls and chaos in the disordered SOS model

Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's left passage formula with kappa=4 whereas their fractal dimension is d_s=1.25, and therefore is NOT described by "Stochastic-Loewner-Evolution" (SLE). Optimal droplets with a lateral size between L and 2L have the same fractal dimension as domain walls but an energy that saturates at a value of order O(1) for L->infinity such that arbitrarily large excitations exist which cost only a small amount of energy. Finally it is demonstrated that the sensitivity of the ground state to small changes of order delta in the disorder is subtle: beyond a cross-over length scale L_delta ~ 1/delta the correlations of the perturbed ground state with the unperturbed ground state, rescaled by the roughness, are suppressed and approach zero logarithmically.Comment: 23 pages, 11 figure

Improved Online Algorithm for Fractional Knapsack in the Random Order Model

The fractional knapsack problem is one of the classical problems in combinatorial optimization, which is well understood in the offline setting. However, the corresponding online setting has been handled only briefly in the theoretical computer science literature so far, although it appears in several applications. Even the previously best known guarantee for the competitive ratio was worse than the best known for the integral problem in the popular random order model. We show that there is an algorithm for the online fractional knapsack problem that admits a competitive ratio of 4.39. Our result significantly improves over the previously best known competitive ratio of 9.37 and surpasses the current best 6.65-competitive algorithm for the integral case. Moreover, our algorithm is deterministic in contrast to the randomized algorithms achieving the results mentioned above

An Integer Interior Point Method for Min-Cost Flow Using Arc Contractions and Deletions

We present an interior point method for the min-cost flow problem that uses arc contractions and deletions to steer clear from the boundary of the polytope when path-following methods come too close. We obtain a randomized algorithm running in expected $\tilde O( m^{3/2} )$ time that only visits integer lattice points in the vicinity of the central path of the polytope. This enables us to use integer arithmetic like classical combinatorial algorithms typically do. We provide explicit bounds on the size of the numbers that appear during all computations. By presenting an integer arithmetic interior point algorithm we avoid the tediousness of floating point error analysis and achieve a method that is guaranteed to be free of any numerical issues. We thereby eliminate one of the drawbacks of numerical methods in contrast to combinatorial min-cost flow algorithms that still yield the most efficient implementations in practice, despite their inferior worst-case time complexity

Physarum Inspired Dynamics to Solve Semi-Definite Programs

Physarum Polycephalum is a Slime mold that can solve the shortest path problem. A mathematical model based on the Physarum's behavior, known as the Physarum Directed Dynamics, can solve positive linear programs. In this paper, we will propose a Physarum based dynamic based on the previous work and introduce a new way to solve positive Semi-Definite Programming (SDP) problems, which are more general than positive linear programs. Empirical results suggest that this extension of the dynamic can solve the positive SDP showing that the nature-inspired algorithm can solve one of the hardest problems in the polynomial domain. In this work, we will formulate an accurate algorithm to solve positive and some non-negative SDPs and formally prove some key characteristics of this solver thus inspiring future work to try and refine this method

An Integer Interior Point Method for Min-Cost Flow Using Arc Contractions and Deletions

We present an interior point method for the min-cost flow problem that uses arc contractions and deletions to steer clear from the boundary of the polytope when path-following methods come too close. We obtain a randomized algorithm running in expected $\tilde O( m^{3/2} )$ time that only visits integer lattice points in the vicinity of the central path of the polytope. This enables us to use integer arithmetic like classical combinatorial algorithms typically do. We provide explicit bounds on the size of the numbers that appear during all computations. By presenting an integer arithmetic interior point algorithm we avoid the tediousness of floating point error analysis and achieve a method that is guaranteed to be free of any numerical issues. We thereby eliminate one of the drawbacks of numerical methods in contrast to combinatorial min-cost flow algorithms that still yield the most efficient implementations in practice, despite their inferior worst-case time complexity

Near-Optimal Approximate Shortest Paths and Transshipment in Distributed and Streaming Models

We present a method for solving the shortest transshipment problem-also known as uncapacitated minimum cost flow-up to a multiplicative error of 1 + ϵ in undirected graphs with non-negative integer edge weights using a tailored gradient descent algorithm. Our gradient descent algorithm takes ϵ-3 polylog n iterations, and in each iteration it needs to solve an instance of the transshipment problem up to a multiplicative error of polylog n, where n is the number of nodes. In particular, this allows us to perform a single iteration by computing a solution on a sparse spanner of logarithmic stretch. Using a careful white-box analysis, we can further extend the method to finding approximate solutions for the single-source shortest paths (SSSP) problem. As a consequence, we improve prior work by obtaining the following results: 1. Broadcast CONGEST model: (1+")-approximate SSSP using Õ((√ n+D) · ϵ-O(1)) rounds, 1 where D is the (hop) diameter of the network. 2. Broadcast congested clique model: (1+ϵ)-approximate shortest transshipment and SSSP using Õ (ϵ-O(1)) rounds. 3. Multipass streaming model: (1+ϵ)-approximate shortest transshipment and SSSP using Õ (n) space and Õ(ϵ-O(1)) passes. The previously fastest SSSP algorithms for these models leverage sparse hop sets. We bypass the hop set construction; computing a spanner is sufficient with our method. The above bounds assume non-negative integer edge weights that are polynomially bounded in n; for general nonnegative weights, running times scale with the logarithm of the maximum ratio between non-zero weights. In case of asymmetric costs for traversing an edge in opposite directions, running times scale with the maximum ratio between the costs of both directions over all edges

Near-Optimal Distributed Maximum Flow

We present a near-optimal distributed algorithm for $(1+o(1))$-approximation of single-commodity maximum flow in undirected weighted networks that runs in $(D+ \sqrt{n})\cdot n^{o(1)}$ communication rounds in the \Congest model. Here, $n$ and $D$ denote the number of nodes and the network diameter, respectively. This is the first improvement over the trivial bound of $O(n^2)$, and it nearly matches the $\tilde{\Omega}(D+ \sqrt{n})$ round complexity lower bound. The development of the algorithm contains two results of independent interest: (i) A $(D+\sqrt{n})\cdot n^{o(1)}$-round distributed construction of a spanning tree of average stretch $n^{o(1)}$. (ii) A $(D+\sqrt{n})\cdot n^{o(1)}$-round distributed construction of an $n^{o(1)}$-congestion approximator consisting of the cuts induced by $O(\log n)$ virtual trees. The distributed representation of the cut approximator allows for evaluation in $(D+\sqrt{n})\cdot n^{o(1)}$ rounds. All our algorithms make use of randomization and succeed with high probability

Similar familial risk in multiple sclerosis subgroups Introduction

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Glucosylceramide is synthesized at the cytosolic surface of various Golgi subfractions

In our attempt to assess the topology of glucosylceramide biosynthesis, we have employed a truncated ceramide analogue that permeates cell membranes and is converted into water soluble sphingolipid analogues both in living and in fractionated cells. Truncated sphingomyelin is synthesized in the lumen of the Golgi, whereas glucosylceramide is synthesized at the cytosolic surface of the Golgi as shown by (a) the insensitivity of truncated sphingomyelin synthesis and the sensitivity of truncated glucosylceramide synthesis in intact Golgi membranes from rabbit liver to treatment with protease or the chemical reagent DIDS; and (b) sensitivity of truncated sphingomyelin export and insensitivity of truncated glucosylceramide export to decreased temperature and the presence of GTP-γ-S in semiintact CHO cells. Moreover, subfractionation of rat liver Golgi demonstrated that the sphingomyelin synthase activity was restricted to fractions containing marker enzymes for the proximal Golgi, whereas the capacity to synthesize truncated glucosylceramide was also found in fractions containing distal Golgi markers. A similar distribution of glucosylceramide synthesizing activity was observed in the Golgi of the human liver derived HepG2 cells. The cytosolic orientation of the reaction in HepG2 cells was confirmed by complete extractability of newly formed NBD-glucosylceramide from isolated Golgi membranes or semiintact cells by serum albumin, whereas NBD-sphingomyelin remained protected against such extraction

Plasma neurofilament light chain concentration is increased in anorexia nervosa

Anorexia nervosa (AN) is a severe psychiatric disorder with high mortality and, to a large extent, unknown pathophysiology. Structural brain differences, such as global or focal reductions in grey or white matter volumes, as well as enlargement of the sulci and the ventricles, have repeatedly been observed in individuals with AN. However, many of the documented aberrances normalize with weight recovery, even though some studies show enduring changes. To further explore whether AN is associated with neuronal damage, we analysed the levels of neurofilament light chain (NfL), a marker reflecting ongoing neuronal injury, in plasma samples from females with AN, females recovered from AN (AN-REC) and normal-weight age-matched female controls (CTRLS). We detected significantly increased plasma levels of NfL in AN vs CTRLS (medianAN = 15.6 pg/ml, IQRAN = 12.1-21.3, medianCTRL = 9.3 pg/ml, IQRCTRL = 6.4-12.9, and p < 0.0001), AN vs AN-REC (medianAN-REC = 11.1 pg/ml, IQRAN-REC = 8.6-15.5, and p < 0.0001), and AN-REC vs CTRLS (p = 0.004). The plasma levels of NfL are negatively associated with BMI overall samples (β (±se) = -0.62 ± 0.087 and p = 6.9‧10-12). This indicates that AN is associated with neuronal damage that partially normalizes with weight recovery. Further studies are needed to determine which brain areas are affected, and potential long-term sequelae