A comparison of Monte Carlo generators

A comparison of GENIE, NEUT, NUANCE, and NuWro Monte Carlo neutrino event generators is presented using a set of four observables: protons multiplicity, total visible energy, most energetic proton momentum, and $\pi^+$ two-dimensional energy vs cosine distribution.Comment: 5 pages, 12 figures, Talk given at NUINT12: Eighth International Workshop on Neutrino-Nucleus Interactions in the Few-GeV Region, October 22-27, 2012, Rio de Janeiro, Brasi

The Streaming k-Mismatch Problem: Tradeoffs Between Space and Total Time

We revisit the $k$-mismatch problem in the streaming model on a pattern of length $m$ and a streaming text of length $n$, both over a size-$\sigma$ alphabet. The current state-of-the-art algorithm for the streaming $k$-mismatch problem, by Clifford et al. [SODA 2019], uses $\tilde O(k)$ space and $\tilde O\big(\sqrt k\big)$ worst-case time per character. The space complexity is known to be (unconditionally) optimal, and the worst-case time per character matches a conditional lower bound. However, there is a gap between the total time cost of the algorithm, which is $\tilde O(n\sqrt k)$, and the fastest known offline algorithm, which costs $\tilde O\big(n + \min\big(\frac{nk}{\sqrt m},\sigma n\big)\big)$ time. Moreover, it is not known whether improvements over the $\tilde O(n\sqrt k)$ total time are possible when using more than $O(k)$ space. We address these gaps by designing a randomized streaming algorithm for the $k$-mismatch problem that, given an integer parameter $k\le s \le m$, uses $\tilde O(s)$ space and costs $\tilde O\big(n+\min\big(\frac {nk^2}m,\frac{nk}{\sqrt s},\frac{\sigma nm}s\big)\big)$ total time. For $s=m$, the total runtime becomes $\tilde O\big(n + \min\big(\frac{nk}{\sqrt m},\sigma n\big)\big)$, which matches the time cost of the fastest offline algorithm. Moreover, the worst-case time cost per character is still $\tilde O\big(\sqrt k\big)$.Comment: Extended abstract to appear in CPM 202

Improved Circular k-Mismatch Sketches

The shift distance $\mathsf{sh}(S_1,S_2)$ between two strings $S_1$ and $S_2$ of the same length is defined as the minimum Hamming distance between $S_1$ and any rotation (cyclic shift) of $S_2$. We study the problem of sketching the shift distance, which is the following communication complexity problem: Strings $S_1$ and $S_2$ of length $n$ are given to two identical players (encoders), who independently compute sketches (summaries) $\mathtt{sk}(S_1)$ and $\mathtt{sk}(S_2)$, respectively, so that upon receiving the two sketches, a third player (decoder) is able to compute (or approximate) $\mathsf{sh}(S_1,S_2)$ with high probability. This paper primarily focuses on the more general $k$-mismatch version of the problem, where the decoder is allowed to declare a failure if $\mathsf{sh}(S_1,S_2)>k$, where $k$ is a parameter known to all parties. Andoni et al. (STOC'13) introduced exact circular $k$-mismatch sketches of size $\widetilde{O}(k+D(n))$, where $D(n)$ is the number of divisors of $n$. Andoni et al. also showed that their sketch size is optimal in the class of linear homomorphic sketches. We circumvent this lower bound by designing a (non-linear) exact circular $k$-mismatch sketch of size $\widetilde{O}(k)$; this size matches communication-complexity lower bounds. We also design $(1\pm \varepsilon)$-approximate circular $k$-mismatch sketch of size $\widetilde{O}(\min(\varepsilon^{-2}\sqrt{k}, \varepsilon^{-1.5}\sqrt{n}))$, which improves upon an $\widetilde{O}(\varepsilon^{-2}\sqrt{n})$-size sketch of Crouch and McGregor (APPROX'11)

The GENIE Neutrino Monte Carlo Generator: Physics and User Manual

GENIE is a suite of products for the experimental neutrino physics community. This suite includes i) a modern software framework for implementing neutrino event generators, a state-of-the-art comprehensive physics model and tools to support neutrino interaction simulation for realistic experimental setups (the Generator product), ii) extensive archives of neutrino, charged-lepton and hadron scattering data and software to produce a comprehensive set of data/MC comparisons (the Comparisons product), and iii) a generator tuning framework and fitting applications (the Tuning product). This book provides the definite guide for the GENIE Generator: It presents the software architecture and a detailed description of its physics model and official tunes. In addition, it provides a rich set of data/MC comparisons that characterise the physics performance of GENIE. Detailed step-by-step instructions on how to install and configure the Generator, run its applications and analyze its outputs are also included

Final State Interactions Effects in Neutrino-Nucleus Interactions

Final State Interactions effects are discussed in the context of Monte Carlo simulations of neutrino-nucleus interactions. A role of Formation Time is explained and several models describing this effect are compared. Various observables which are sensitive to FSI effects are reviewed including pion-nucleus interaction and hadron yields in backward hemisphere. NuWro Monte Carlo neutrino event generator is described and its ability to understand neutral current $\pi^0$ production data in $\sim 1$ GeV neutrino flux experiments is demonstrated.Comment: 13 pages, 16 figure

The SMRD subdetector at the T2K near detector station

The T2K long-baseline neutrino oscillation experiment is running in Japan. The primary goals of the T2K are measurement of the mixing angle 13, and precise measurements of the mixing angle 23 and of the mass difference m2 23. The installation of the near detector complex was completed and first data were already registered. This article presents operation of the Side Muon Range Detector, a component of the Off-Axis near detector. Detector concept and implementation are presented, followed by a description of cosmic muon track reconstruction algorithm and finally current status

Time-Space Tradeoffs for Finding a Long Common Substring

We consider the problem of finding, given two documents of total length $n$, a longest string occurring as a substring of both documents. This problem, known as the Longest Common Substring (LCS) problem, has a classic $O(n)$-time solution dating back to the discovery of suffix trees (Weiner, 1973) and their efficient construction for integer alphabets (Farach-Colton, 1997). However, these solutions require $\Theta(n)$ space, which is prohibitive in many applications. To address this issue, Starikovskaya and Vildh{\o}j (CPM 2013) showed that for $n^{2/3} \le s \le n^{1-o(1)}$, the LCS problem can be solved in $O(s)$ space and $O(\frac{n^2}{s})$ time. Kociumaka et al. (ESA 2014) generalized this tradeoff to $1 \leq s \leq n$, thus providing a smooth time-space tradeoff from constant to linear space. In this paper, we obtain a significant speed-up for instances where the length $L$ of the sought LCS is large. For $1 \leq s \leq n$, we show that the LCS problem can be solved in $O(s)$ space and $\tilde{O}(\frac{n^2}{L\cdot s}+n)$ time. The result is based on techniques originating from the LCS with Mismatches problem (Flouri et al., 2015; Charalampopoulos et al., CPM 2018), on space-efficient locally consistent parsing (Birenzwige et al., SODA 2020), and on the structure of maximal repetitions (runs) in the input documents

An Improved Algorithm for The k-Dyck Edit Distance Problem

A Dyck sequence is a sequence of opening and closing parentheses (of various types) that is balanced. The Dyck edit distance of a given sequence of parentheses S is the smallest number of edit operations (insertions, deletions, and substitutions) needed to transform S into a Dyck sequence. We consider the threshold Dyck edit distance problem, where the input is a sequence of parentheses S and a positive integer k, and the goal is to compute the Dyck edit distance of S only if the distance is at most k, and otherwise report that the distance is larger than k. Backurs and Onak [PODS'16] showed that the threshold Dyck edit distance problem can be solved in O(n + k^16) time. In this work, we design new algorithms for the threshold Dyck edit distance problem which costs O(n + k^4.544184) time with high probability or O(n + k^4.853059) deterministically. Our algorithms combine several new structural properties of the Dyck edit distance problem, a refined algorithm for fast (min, +) matrix product, and a careful modification of ideas used in Valiant's parsing algorithm