1,343 research outputs found
Weighted k-Server Bounds via Combinatorial Dichotomies
The weighted -server problem is a natural generalization of the -server
problem where each server has a different weight. We consider the problem on
uniform metrics, which corresponds to a natural generalization of paging. Our
main result is a doubly exponential lower bound on the competitive ratio of any
deterministic online algorithm, that essentially matches the known upper bounds
for the problem and closes a large and long-standing gap.
The lower bound is based on relating the weighted -server problem to a
certain combinatorial problem and proving a Ramsey-theoretic lower bound for
it. This combinatorial connection also reveals several structural properties of
low cost feasible solutions to serve a sequence of requests. We use this to
show that the generalized Work Function Algorithm achieves an almost optimum
competitive ratio, and to obtain new refined upper bounds on the competitive
ratio for the case of different weight classes.Comment: accepted to FOCS'1
cpRAS: a novel circularly permuted RAS-like GTPase domain with a highly scattered phylogenetic distribution
A recent systematic survey suggested that the YRG (or YawG/YlqF) family with the G4-G5-G1-G2-G3 order of the conserved GTPase motifs represents the only possible circularly permuted variation of the canonical GTPase structure. Here we show that a different circularly permuted GTPase domain actually does exist, conforming to the pattern G3-G4-G5-G1-G2. The domain, dubbed cpRAS, is a variant of RAS family GTPases and occurs in two types of larger proteins, either inserted into a region homologous to a bacterial group of proteins classified as COG2373 and potentially related to the alpha-2-macroglobulin family (so far a single protein in Dictyostelium) or in combination with a von Willebrand factor type A (VWA) domain. For the latter protein type, which was found in a few metazoans and several distantly related protists, existence in the common ancestor of opisthokonts, Amoebozoa and excavates followed by at least eight independent losses may be inferred. Our findings thus bring further evidence for the importance of parallel reduction of ancestral complexity in the eukaryotic evolution
Higher-order Erdos--Szekeres theorems
Let P=(p_1,p_2,...,p_N) be a sequence of points in the plane, where
p_i=(x_i,y_i) and x_1<x_2<...<x_N. A famous 1935 Erdos--Szekeres theorem
asserts that every such P contains a monotone subsequence S of
points. Another, equally famous theorem from the same paper implies that every
such P contains a convex or concave subsequence of points.
Monotonicity is a property determined by pairs of points, and convexity
concerns triples of points. We propose a generalization making both of these
theorems members of an infinite family of Ramsey-type results. First we define
a (k+1)-tuple to be positive if it lies on the graph of a
function whose kth derivative is everywhere nonnegative, and similarly for a
negative (k+1)-tuple. Then we say that is kth-order monotone if
its (k+1)-tuples are all positive or all negative.
We investigate quantitative bound for the corresponding Ramsey-type result
(i.e., how large kth-order monotone subsequence can be guaranteed in every
N-point P). We obtain an lower bound ((k-1)-times
iterated logarithm). This is based on a quantitative Ramsey-type theorem for
what we call transitive colorings of the complete (k+1)-uniform hypergraph; it
also provides a unified view of the two classical Erdos--Szekeres results
mentioned above.
For k=3, we construct a geometric example providing an upper
bound, tight up to a multiplicative constant. As a consequence, we obtain
similar upper bounds for a Ramsey-type theorem for order-type homogeneous
subsets in R^3, as well as for a Ramsey-type theorem for hyperplanes in R^4
recently used by Dujmovic and Langerman.Comment: Contains a counter example of Gunter Rote which gives a reply for the
problem number 5 in the previous versions of this pape
Impedance and Instability Studies in LEIR with Xenon
In 2017, the LEIR accelerator has been operated with Xe39+ beam for fixed target experiments in the SPS North Area. The different ion species, with respect to the standard Pb54+, allowed for additional comparative measurements of tune shift versus intensity at injection energy both in coasting and bunched beams. The fast transverse instability observed for high accumulated intensities has been as well characterized and additional observations relevant to impedance have been collected from longitudinal Schottky signal and BTF measurements. The results of these measurements are summarised and compared to the currently developed machine impedance model
Competitive algorithms for generalized k-server in uniform metrics
The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server si lies in its own metric space Mi. A request is a k-tuple r = (r1, r2, âŠâ, rk), which is served by moving some server si to the point ri â Mi, and the goal is to minimize the total distance traveled by the servers. Despite much work, no f(k)-competitive algorithm is known for the problem for k > 2 servers, even for special cases such as uniform metrics and lines. Here, we consider the problem in uniform metrics and give the first f(k)-competitive algorithms for general k. In particular, we obtain deterministic and randomized algorithms with competitive ratio k · 2k and O(k3logâk) respectively. Our deterministic bound is based on a novel application of the polynomial method to online algorithms, and essentially matches the long-known lower bound of 2k â 1. We also give a (2^{2^{O(k)}} ) -competitive deterministic algorithm for weighted uniform metrics, which also essentially matches the recent doubly exponential lower bound for the problem
Learning-augmented dynamic power management with multiple states via new ski rental bounds
No abstract availabl
Better Bounds for Online Line Chasing
We study online competitive algorithms for the line chasing problem in Euclidean spaces R^d, where the input consists of an initial point P_0 and a sequence of lines X_1, X_2, ..., X_m, revealed one at a time. At each step t, when the line X_t is revealed, the algorithm must determine a point P_t in X_t. An online algorithm is called c-competitive if for any input sequence the path P_0, P_1..., P_m it computes has length at most c times the optimum path. The line chasing problem is a variant of a more general convex body chasing problem, where the sets X_t are arbitrary convex sets.
To date, the best competitive ratio for the line chasing problem was 28.1, even in the plane. We improve this bound by providing a simple 3-competitive algorithm for any dimension d. We complement this bound by a matching lower bound for algorithms that are memoryless in the sense of our algorithm, and a lower bound of 1.5358 for arbitrary algorithms. The latter bound also improves upon the previous lower bound of sqrt{2}~=1.412 for convex body chasing in 2 dimensions
Preface to Session 70 " Mathematical models and methods to investigate heterogeneity in cell and cell population biology ": Presentation of Session 70 in ICNAAM 2015, Rhodes
International audienceThis session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria
Differentially private correlation clustering
Correlation clustering is a widely used technique
in unsupervised machine learning. Motivated by
applications where individual privacy is a concern,
we initiate the study of differentially private correlation
clustering. We propose an algorithm that
achieves subquadratic additive error compared
to the optimal cost. In contrast, straightforward
adaptations of existing non-private algorithms all
lead to a trivial quadratic error. Finally, we give
a lower bound showing that any pure differentially
private algorithm for correlation clustering
requires additive error of Ω (n).http://proceedings.mlr.press/v139/bun21a.htm
Competitive Algorithms for Generalized k-Server in Uniform Metrics
The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server lies in its own metric space . A request is a k-tuple and to serve it, we need to move some server to the point , and the goal is to minimize the total distance traveled by the servers. Despite much work, no f(k)-competitive algorithm is known for the problem for k > 2 servers, even for special cases such as uniform metrics and lines. Here, we consider the problem in uniform metrics and give the first f(k)-competitive algorithms for general k. In particular, we obtain deterministic and randomized algorithms with competitive ratio and respectively. Our deterministic bound is based on a novel application of the polynomial method to online algorithms, and essentially matches the long-known lower bound of . We also give a -competitive deterministic algorithm for weighted uniform metrics, which also essentially matches the recent doubly exponential lower bound for the problem
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