arXiv subjects

Sebastian Wild

Publications and source records attributed to Sebastian Wild.

At least 55 records · Page 3Linked to original sources

arXiv2018

Average Cost of QuickXsort with Pivot Sampling

QuickXsort is a strategy to combine Quicksort with another sorting method X, so that the result has essentially the same comparison cost as X in isolation, but sorts in place even when X requires a linear-size buffer. We solve the recurrence for QuickXsort precisely up to the linear term including the optimization to choose pivots from a sample of k elements. This allows to immediately obtain overall average costs using only the average costs of sorting method X (as if run in isolation). We thereby extend and greatly simplify the analysis of QuickHeapsort and QuickMergesort with practically efficient pivot selection, and give the first tight upper bounds including the linear term for such methods.

cs.DS↗

arXiv2018

Nearly-Optimal Mergesorts: Fast, Practical Sorting Methods That Optimally Adapt to Existing Runs

We present two stable mergesort variants, "peeksort" and "powersort", that exploit existing runs and find nearly-optimal merging orders with practically negligible overhead. Previous methods either require substantial effort for determining the merging order (Takaoka 2009; Barbay & Navarro 2013) or do not have a constant-factor optimal worst-case guarantee (Peters 2001; Auger, Nicaud & Pivoteau 2015; Buss & Knop 2018). We demonstrate that our methods are competitive in terms of running time with state-of-the-art implementations of stable sorting methods.

cs.DS↗

arXiv2018

BBN constraints on MeV-scale dark sectors. Part I. Sterile decays

We study constraints from Big Bang Nucleosynthesis on inert particles in a dark sector which contribute to the Hubble rate and therefore change the predictions of the primordial nuclear abundances. We pay special attention to the case of MeV-scale particles decaying into dark radiation, which are neither fully relativistic nor non-relativistic during all temperatures relevant to Big Bang Nucleosynthesis. As an application we discuss the implications of our general results for models of self-interacting dark matter with light mediators.

hep-ph↗

arXiv2018

Halo-independent comparison of direct detection experiments in the effective theory of dark matter-nucleon interactions

The theoretical interpretation of dark matter direct detection experiments is hindered by uncertainties of the microphysics governing the dark matter-nucleon interaction, and of the dark matter density and velocity distribution inside the Solar System. These uncertainties are especially relevant when confronting a detection claim to the null results from other experiments, since seemingly conflicting experimental results may be reconciled when relaxing the assumptions about the form of the interaction and/or the velocity distribution. We present in this paper a halo-independent method to calculate the maximum number of events in a direct detection experiment given a set of null search results, allowing for the first time the scattering to be mediated by an arbitrary combination of various interactions (concretely we consider up to 64). We illustrate this method to examine the compatibility of the dark matter interpretation of the three events detected by the silicon detectors in the CDMS-II experiment with the null results from XENON1T and PICO-60.

hep-ph↗

arXiv2018

DarkBit: A GAMBIT module for computing dark matter observables and likelihoods

We introduce DarkBit, an advanced software code for computing dark matter constraints on various extensions to the Standard Model of particle physics, comprising both new native code and interfaces to external packages. This release includes a dedicated signal yield calculator for gamma-ray observations, which significantly extends current tools by implementing a cascade decay Monte Carlo, as well as a dedicated likelihood calculator for current and future experiments (gamlike). This provides a general solution for studying complex particle physics models that predict dark matter annihilation to a multitude of final states. We also supply a direct detection package that models a large range of direct detection experiments (DDcalc), and provides the corresponding likelihoods for arbitrary combinations of spin-independent and spin-dependent scattering processes. Finally, we provide custom relic density routines along with interfaces to DarkSUSY, micrOMEGAs, and the neutrino telescope likelihood package nuLike. DarkBit is written in the framework of the Global And Modular Beyond the Standard Model Inference Tool (GAMBIT), providing seamless integration into a comprehensive statistical fitting framework that allows users to explore new models with both particle and astrophysics constraints, and a consistent treatment of systematic uncertainties. In this paper we describe its main functionality, provide a guide to getting started quickly, and show illustrative examples for results obtained with DarkBit (both as a standalone tool and as a GAMBIT module). This includes a quantitative comparison between two of the main dark matter codes (DarkSUSY and micrOMEGAs), and application of DarkBit's advanced direct and indirect detection routines to a simple effective dark matter model.

hep-ph↗

arXiv2017

Dark matter self-interactions from a general spin-0 mediator

Dark matter particles interacting via the exchange of very light spin-0 mediators can have large self-interaction rates and obtain their relic abundance from thermal freeze-out. At the same time, these models face strong bounds from direct and indirect probes of dark matter as well as a number of constraints on the properties of the mediator. We investigate whether these constraints can be consistent with having observable effects from dark matter self-interactions in astrophysical systems. For the case of a mediator with purely scalar couplings we point out the highly relevant impact of low-threshold direct detection experiments like CRESST-II, which essentially rule out the simplest realization of this model. These constraints can be significantly relaxed if the mediator has CP-violating couplings, but then the model faces strong constraints from CMB measurements, which can only be avoided in special regions of parameter space.

hep-ph↗

arXiv2017

A Practical and Worst-Case Efficient Algorithm for Divisor Methods of Apportionment

Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms that implement divisor methods: one by Cheng and Eppstein (ISAAC, 2014) has worst-case optimal running time but is complex, while the other (Pukelsheim, 2014) is relatively simple and fast in practice but does not offer worst-case guarantees. We demonstrate that the former algorithm is much slower than the other in practice and propose a novel algorithm that avoids the shortcomings of both. We investigate the running-time behavior of the three contenders in order to determine which is most useful in practice.

cs.DS↗

arXiv2017

Exploring light mediators with low-threshold direct detection experiments

We explore the potential of future cryogenic direct detection experiments to determine the properties of the mediator that communicates the interactions between dark matter and nuclei. Due to their low thresholds and large exposures, experiments like CRESST-III, SuperCDMS SNOLAB and EDELWEISS-III will have excellent capability to reconstruct mediator masses in the MeV range for a large class of models. Combining the information from several experiments further improves the parameter reconstruction, even when taking into account additional nuisance parameters related to background uncertainties and the dark matter velocity distribution. These observations may offer the intriguing possibility of studying dark matter self-interactions with direct detection experiments.

hep-ph↗

arXiv2017

Efficient Algorithms for Envy-Free Stick Division With Fewest Cuts

Given a set of n sticks of various (not necessarily different) lengths, what is the largest length so that we can cut k equally long pieces of this length from the given set of sticks? We analyze the structure of this problem and show that it essentially reduces to a single call of a selection algorithm; we thus obtain an optimal linear-time algorithm. This algorithm also solves the related envy-free stick-division problem, which Segal-Halevi, Hassidim, and Aumann (AAMAS, 2015) recently used as their central primitive operation for the first discrete and bounded envy-free cake cutting protocol with a proportionality guarantee when pieces can be put to waste.

cs.DS↗

arXiv2017

GAMBIT: The Global and Modular Beyond-the-Standard-Model Inference Tool

We describe the open-source global fitting package GAMBIT: the Global And Modular Beyond-the-Standard-Model Inference Tool. GAMBIT combines extensive calculations of observables and likelihoods in particle and astroparticle physics with a hierarchical model database, advanced tools for automatically building analyses of essentially any model, a flexible and powerful system for interfacing to external codes, a suite of different statistical methods and parameter scanning algorithms, and a host of other utilities designed to make scans faster, safer and more easily-extendible than in the past. Here we give a detailed description of the framework, its design and motivation, and the current models and other specific components presently implemented in GAMBIT. Accompanying papers deal with individual modules and present first GAMBIT results. GAMBIT can be downloaded from gambit.hepforge.org.

hep-ph↗

arXiv2017

Quicksort Is Optimal For Many Equal Keys

I prove that the average number of comparisons for median-of-$k$ Quicksort (with fat-pivot a.k.a. three-way partitioning) is asymptotically only a constant $α_k$ times worse than the lower bound for sorting random multisets with $Ω(n^\varepsilon)$ duplicates of each value (for any $\varepsilon>0$). The constant is $α_k = \ln(2) / \bigl(H_{k+1}-H_{(k+1)/2} \bigr)$, which converges to 1 as $k\to\infty$, so Quicksort is asymptotically optimal for inputs with many duplicates. This resolves a conjecture by Sedgewick and Bentley (1999, 2002) and constitutes the first progress on the analysis of Quicksort with equal elements since Sedgewick's 1977 article.

cs.DS↗

arXiv2017

Antideuterons in cosmic rays: sources and discovery potential

Antibaryons are produced in our Galaxy in collisions of high energy cosmic rays with the interstellar medium and in old supernova remnants, and possibly, in exotic sources such as primordial black hole evaporation or dark matter annihilations and decays. The search for signals from exotic sources in antiproton data is hampered by large backgrounds from spallation which, within theoretical errors, can solely account for the current data. Due to the higher energy threshold for antideuteron production, which translates into a suppression of the low energy flux from spallations, antideuteron searches have been proposed as a probe for exotic sources. We perform in this paper a comprehensive analysis of the antideuteron fluxes at the Earth expected from known and hypothetical sources in our Galaxy, and we calculate their maximal values consistent with current antiproton data from AMS-02. We find that supernova remnants generate a negligible flux, whereas primordial black hole evaporation and dark matter annihilations or decays may dominate the total flux at low energies. On the other hand, we find that the detection of cosmic antideuterons would require, for the scenarios studied in this paper and assuming optimistic values of the coalescence momentum and solar modulation, an increase of the experimental sensitivity compared to ongoing and planned instruments by at least a factor of 2. Finally, we briefly comment on the prospects for antihelium-3 detection.

astro-ph.HE↗

arXiv2017

Studying generalised dark matter interactions with extended halo-independent methods

The interpretation of dark matter direct detection experiments is complicated by the fact that neither the astrophysical distribution of dark matter nor the properties of its particle physics interactions with nuclei are known in detail. To address both of these issues in a very general way we develop a new framework that combines the full formalism of non-relativistic effective interactions with state-of-the-art halo-independent methods. This approach makes it possible to analyse direct detection experiments for arbitrary dark matter interactions and quantify the goodness-of-fit independent of astrophysical uncertainties. We employ this method in order to demonstrate that the degeneracy between astrophysical uncertainties and particle physics unknowns is not complete. Certain models can be distinguished in a halo-independent way using a single ton-scale experiment based on liquid xenon, while other models are indistinguishable with a single experiment but can be separated using combined information from several target elements.

hep-ph↗

arXiv2016

Why Is Dual-Pivot Quicksort Fast?

I discuss the new dual-pivot Quicksort that is nowadays used to sort arrays of primitive types in Java. I sketch theoretical analyses of this algorithm that offer a possible, and in my opinion plausible, explanation why (a) dual-pivot Quicksort is faster than the previously used (classic) Quicksort and (b) why this improvement was not already found much earlier.

cs.DS↗

arXiv2016

DAMA confronts null searches in the effective theory of dark matter-nucleon interactions

We examine the dark matter interpretation of the modulation signal reported by the DAMA experiment from the perspective of effective field theories displaying Galilean invariance. We consider the most general effective coupling leading to the elastic scattering of a dark matter particle with spin 0 or 1/2 off a nucleon, and we analyze the compatibility of the DAMA signal with the null results from other direct detection experiments, as well as with the non-observation of a high energy neutrino flux in the direction of the Sun from dark matter annihilation. To this end, we develop a novel semi-analytical approach for comparing experimental results in the high-dimensional parameter space of the non-relativistic effective theory. Assuming the standard halo model, we find a strong tension between the dark matter interpretation of the DAMA modulation signal and the null result experiments. We also list possible ways-out of this conclusion.

hep-ph↗

arXiv2016

Signatures from Scalar Dark Matter with a Vector-like Quark Mediator

We present a comprehensive study of a model where the dark matter is composed of a singlet real scalar that couples to the Standard Model predominantly via a Yukawa interaction with a light quark and a colored vector-like fermion. A distinctive feature of this scenario is that thermal freeze-out in the early universe may be driven by annihilation both into gluon pairs at one-loop ($gg$) and by virtual internal Bremsstrahlung of a gluon ($q \bar{q} g$). Such a dark matter candidate may also be tested through direct and indirect detection and at the LHC; viable candidates have either a mass nearly degenerate with that of the fermionic mediator or a mass above about 2 TeV.

hep-ph↗

arXiv2015

A novel approach to derive halo-independent limits on dark matter properties

We propose a method that allows to place an upper limit on the dark matter elastic scattering cross section with nucleons which is independent of the velocity distribution. Our approach combines null results from direct detection experiments with indirect searches at neutrino telescopes, and goes beyond previous attempts to remove astrophysical uncertainties in that it directly constrains the particle physics properties of the dark matter. The resulting halo-independent upper limits on the scattering cross section of dark matter are remarkably strong and reach $σ_{\text{SI}}^{p} \lesssim 10^{-43} \, (10^{-42})~\text{cm}^2$ and $σ_{\text{SD}}^{p} \lesssim 10^{-37} \, (3\times 10^{-37 })~\text{cm}^2$, for dark matter particles of $m_{\text{DM}}\sim 1~\text{TeV}$ annihilating into $W^+W^-$ ($b\bar b$), assuming $ρ_\text{loc}=0.3\text{ GeV}/\text{cm}^3$.

hep-ph↗

arXiv2015

Analysis of Pivot Sampling in Dual-Pivot Quicksort

The new dual-pivot Quicksort by Vladimir Yaroslavskiy - used in Oracle's Java runtime library since version 7 - features intriguing asymmetries. They make a basic variant of this algorithm use less comparisons than classic single-pivot Quicksort. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order statistics of a random sample. Surprisingly, dual-pivot Quicksort then needs more comparisons than a corresponding version of classic Quicksort, so it is clear that counting comparisons is not sufficient to explain the running time advantages observed for Yaroslavskiy's algorithm in practice. Consequently, we take a more holistic approach and give also the precise leading term of the average number of swaps, the number of executed Java Bytecode instructions and the number of scanned elements, a new simple cost measure that approximates I/O costs in the memory hierarchy. We determine optimal order statistics for each of the cost measures. It turns out that the asymmetries in Yaroslavskiy's algorithm render pivots with a systematic skew more efficient than the symmetric choice. Moreover, we finally have a convincing explanation for the success of Yaroslavskiy's algorithm in practice: Compared with corresponding versions of classic single-pivot Quicksort, dual-pivot Quicksort needs significantly less I/Os, both with and without pivot sampling.

cs.DS↗