The Complexity of Flow Expansion and Electrical Flow Expansion

FlowExpansion is a network design problem, in which the input consists of a flow network and a set of candidate edges, which may be added to the network. Adding a candidate incurs given costs. The goal is to determine the cheapest set of candidate edges that, if added, allow the demands to be satisfied. FlowExpansion is a variant of the Minimum-Cost Flow problem with non-linear edge costs. We study FlowExpansion for both graph-theoretical and electrical flow networks. In the latter case this problem is also known as the Transmission Network Expansion Planning problem. We give a structured view over the complexity of the variants of FlowExpansion that arise from restricting, e.g., the graph classes, the capacities, or the number of sources and sinks. Our goal is to determine which restrictions have a crucial impact on the computational complexity. The results in this paper range from polynomial-time algorithms for the more restricted variants over NP-hardness proofs to proofs that certain variants are NP-hard to approximate even within a logarithmic factor of the optimal solution

Deleterious variants in TRAK1 disrupt mitochondrial movement and cause fatal encephalopathy

This is the author accepted manuscript. The final version is available from Oxford University Press via the DOI in this record.The corrigendum to this article is in ORE: http://hdl.handle.net/10871/33588Cellular distribution and dynamics of mitochondria are regulated by several motor proteins and a microtubule network. In neurons, mitochondrial trafficking is crucial because of high energy needs and calcium ion buffering along axons to synapses during neurotransmission. The trafficking kinesin proteins (TRAKs) are well characterized for their role in lysosomal and mitochondrial trafficking in cells, especially neurons. Using whole exome sequencing, we identified homozygous truncating variants in TRAK1 (NM_001042646:c.287-2A > C), in six lethal encephalopathic patients from three unrelated families. The pathogenic variant results in aberrant splicing and significantly reduced gene expression at the RNA and protein levels. In comparison with normal cells, TRAK1-deficient fibroblasts showed irregular mitochondrial distribution, altered mitochondrial motility, reduced mitochondrial membrane potential, and diminished mitochondrial respiration. This study confirms the role of TRAK1 in mitochondrial dynamics and constitutes the first report of this gene in association with a severe neurodevelopmental disorder.D.M.E. and J.K. are supported by the Office of Naval Research (ONR) Grant N000141410538. M.S. is supported by the BBSRC (BB/K006231/1), a Wellcome Trust Institutional Strategic Support Award (WT097835MF, WT105618MA), and a Marie Curie Initial Training Network (ITN) action PerFuMe (316723). M.C.V.M., J.S., H.P., C.F., T.V. and W.A.G. are supported by the NGHRI Intramural Research Program. G.R. is supported by the Kahn Family Foundation and the Israeli Centers of Excellence (I-CORE) Program (ISF grant no. 41/11)

Evolution of the diatoms: insights from fossil, biological and molecular data

Molecular sequence analyses have yielded many important insights into diatom evolution, but there have been few attempts to relate these to the extensive fossil record of diatoms, probably because of unfamiliarity with the data available, which are scattered widely through the geological literature. We review the main features of molecular phylogenies and concentrate on the correspondence between these and the fossil record; we also review the evolution of major morphological, cytological and life cycle characteristics, and possible diatom origins. The first physical remains of diatoms are from the Jurassic, and well-preserved, diverse floras are available from the Lower Cretaceous. Though these are unequivocally identifiable as centric diatoms, none except a possible Stephanopyxis can be unequivocally linked to lineages of extant diatoms, although it is almost certain that members of the Coscinodiscophyceae (radial centrics) and Mediophyceae (polar centrics) were present; some display curious morphological features that hint at an unorthodox cell division mechanism and life cycle. It seems most likely that the earliest diatoms were marine, but recently discovered fossil deposits hint that episodes of terrestrial colonization may have occurred in the Mesozoic, though the main invasion of freshwaters appears to have been delayed until the Cenozoic. By the Upper Cretaceous, many lineages are present that can be convincingly related to extant diatom taxa. Pennate diatoms appear in the late Cretaceous and raphid diatoms in the Palaeocene, though molecular phylogenies imply that raphid diatoms did in fact evolve considerably earlier. Recent evidence shows that diatoms are substantially underclassified at the species level, with many semicryptic or cryptic species to be recognized; however, there is little prospect of being able to discriminate between such taxa in fossil material

Bounded Memory Active Learning through Enriched Queries

The explosive growth of easily-accessible unlabeled data has lead to growing interest in active learning, a paradigm in which data-hungry learning algorithms adaptively select informative examples in order to lower prohibitively expensive labeling costs. Unfortunately, in standard worst-case models of learning, the active setting often provides no improvement over non-adaptive algorithms. To combat this, a series of recent works have considered a model in which the learner may ask enriched queries beyond labels. While such models have seen success in drastically lowering label costs, they tend to come at the expense of requiring large amounts of memory. In this work, we study what families of classifiers can be learned in bounded memory. To this end, we introduce a novel streaming-variant of enriched-query active learning along with a natural combinatorial strategy called lossless sample compression that is sufficient for learning not only with bounded memory, but in a query-optimal and computationally efficient manner as well. Finally, we give three fundamental examples of classifier families with small, easy to compute lossless compression schemes when given access to basic enriched queries: axis-aligned rectangles, decision trees, and halfspaces in two dimensions

Constructing Near Spanning Trees with Few Local Inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded-degree graph. Given an edge $e$ in $G$ we would like to decide whether $e$ belongs to a connected subgraph $G'$ consisting of $(1+\epsilon)n$ edges (for a prespecified constant $\epsilon >0$), where the decision for different edges should be consistent with the same subgraph $G'$. Can this task be performed by inspecting only a {\em constant} number of edges in $G$? Our main results are: (1) We show that if every $t$-vertex subgraph of $G$ has expansion $1/(\log t)^{1+o(1)}$ then one can (deterministically) construct a sparse spanning subgraph $G'$ of $G$ using few inspections. To this end we analyze a "local" version of a famous minimum-weight spanning tree algorithm. (2) We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of $3$-regular graphs of high girth, in which every $t$-vertex subgraph has expansion $1/(\log t)^{1-o(1)}$

Fixed-Parameter and Approximation Algorithms: A New Look

A Fixed-Parameter Tractable (FPT) ρ-approximation algorithm for a minimization (resp. maximization) parameterized problem P is an FPT algorithm that, given an instance (x,k) ∈ P computes a solution of cost at most k · ρ(k) (resp. k/ρ(k)) if a solution of cost at most (resp. at least) k exists; otherwise the output can be arbitrary. For well-known intractable problems such as the W[1]-hard Clique and W[2]hard Set Cover problems, the natural question is whether we can get any FPT-approximation. It is widely believed that both Clique and Set-Cover admit no FPT ρ-approximation algorithm, for any increasing function ρ. However, to the best of our knowledge, there has been no progress towards proving this conjecture. Assuming standard conjectures such as the Exponential Time Hypothesis (ETH) [19] and the Projection Games Conjecture (PGC) [29], we make the first progress towards proving this conjecture by showing that • Under the ETH and PGC, there exist constants F1,F2> 0 such that the Set Cover problem does not admit a FPT approximation algorithm with ratio k F1 in 2 kF 2 · poly(N,M) time, where N is the size of the universe and M is the number of sets. • Unless NP ⊆ SUBEXP, for every 1> δ> 0 there exists a constant F(δ)> 0 such that Clique has no FPT cost approximation with ratio k1−δ in 2kF · poly(n) time, where n is the number of vertices in the graph. In the second part of the paper we consider various W[1]-hard problems such as Directed Steiner Tree, Directed Steiner Forest, Directed Steiner Network and Minimum Size Edge Cover. For all these problem we give polynomial time f (OPT)-approximation algorithms for some small function f (the largest approximation ratio we give is OPT 2). Our results indicate a potential separation between the classes W[1] and W[2]; since no W[2]-hard problem is known to have a polynomial time f (OPT)-approximation for any function f. Finally, we answer a question by Marx [25] by showing the well-studied Strongly Connected Steiner Subgraph problem (which is W[1]-hard and does not have any polynomial time constant factor approximation) has a constant factor FPT-approximation.