Quantum, Stochastic, and Pseudo Stochastic Languages with Few States

Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all these numbers of states are optimal. After this, we completely characterize the class of languages recognized by 1-state GFAs, which is the only nontrivial class of languages recognized by 1-state automata. Finally, we consider the variations of PFAs, QFAs, and GFAs based on the notion of inclusive/exclusive cutpoint, and present some results on their expressive power.Comment: A new version with new results. Previous version: Arseny M. Shur, Abuzer Yakaryilmaz: Quantum, Stochastic, and Pseudo Stochastic Languages with Few States. UCNC 2014: 327-33

On Global Types and Multi-Party Session

Global types are formal specifications that describe communication protocols in terms of their global interactions. We present a new, streamlined language of global types equipped with a trace-based semantics and whose features and restrictions are semantically justified. The multi-party sessions obtained projecting our global types enjoy a liveness property in addition to the traditional progress and are shown to be sound and complete with respect to the set of traces of the originating global type. Our notion of completeness is less demanding than the classical ones, allowing a multi-party session to leave out redundant traces from an underspecified global type. In addition to the technical content, we discuss some limitations of our language of global types and provide an extensive comparison with related specification languages adopted in different communities

The Equivalence Problem for Deterministic MSO Tree Transducers is Decidable

It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs

The spatial coverage of dairy cattle urine patches in an intensively grazed pasture system

Accurate field data on the paddock area affected by cow urine depositions are critical to the estimation and modelling of nitrogen (N) losses and N management in grazed pasture systems. A new technique using survey-grade global positioning system (GPS) technology was developed to precisely measure the paddock spatial area coverage, diversity and distribution of dairy cattle urine patches in grazed paddocks over time. A 4-year study was conducted on the Lincoln University Dairy Farm (LUDF), Canterbury, New Zealand, from 2003 to 2007. Twelve field plots, each 100m² in area, were established on typical grazing areas of the farm. All urine and dung deposits within the plots were visually identified, the pasture response area (radius) measured and position marked with survey-grade GPS. The plots were grazed as part of the normal grazing rotation of the farm and urine and dung deposits measured at 12-week intervals. The data were collated using spatial (GIS) software and an assessment of annual urine patch coverage and spatial distribution was made. Grazing intensities ranged from 17645 to 30295 cow grazing h/ha/yr. Mean annual areas of urine patches ranged from 0·34 to 0·40m² (4-year mean 0·37±0·009m²), with small but significant variation between years and seasons. Mean annual urine patch numbers were 6240±124 patches/ha/yr. The mean proportional area coverage for a single sampling event or season was 0·058 and the mean proportional annual urine patch coverage was 0·232±0·0071. There was a strong linear relationship between annual cow grazing h/ha and urine patch numbers/ha (R²=0·69) and also annual urine patch area coverage (R²=0·77). Within the stocking densities observed in this study, an annual increase of 10 000 cow grazing h/ha increased urine patch numbers by 1800 urine patches/ha/yr and annual urine patch area coverage by 0·07. This study presents new quantitative data on urine patch size, numbers and the spatial coverage of patches on a temporal basis

Tunneling of massive and charged particles from noncommutative Reissner-Nordstr\"{o}m black hole

Massive charged and uncharged particles tunneling from commutative Reissner-Nordstrom black hole horizon has been studied with details in literature. Here, by adopting the coherent state picture of spacetime noncommutativity, we study tunneling of massive and charged particles from a noncommutative inspired Reissner-Nordstrom black hole horizon. We show that Hawking radiation in this case is not purely thermal and there are correlations between emitted modes. These correlations may provide a solution to the information loss problem. We also study thermodynamics of noncommutative horizon in this setup.Comment: 10 pages, 2 figure

Chrobak Normal Form Revisited, with Applications

Abstract. It is well known that any nondeterministic finite automata over a unary alphabet can be represented in a certain normal form called the Chrobak normal form [1]. We present a very simple conversion pro-cedure working in O(n3) time. Then we extend the algorithm to improve two trade-offs concerning conversions between different representations of unary regular languages. Given an n-state NFA, we are able to find a regular expression of size O ( n2 logn) describing the same language (which improves the previously known O(n2) size bound [8]) and a context-free grammar in Chomsky normal form with O(√n logn) nonterminals (which improves the previously known O(n2/3) bound [3]). As a byproduct of our conversion procedure, we get an alternative proof of the Chrobak normal form theorem. We believe that its efficiency and simplicity make the effort of reproving an already known result worth-while. Key-words: unary automata, descriptional complexity

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Addition of nintedanib or placebo to neoadjuvant gemcitabine and cisplatin in locally advanced muscle-invasive bladder cancer (NEOBLADE) : a double-blind, randomised, phase 2 trial

Background Recurrence is common after neoadjuvant chemotherapy and radical treatment for muscle-invasive bladder cancer. We investigated the effect of adding nintedanib to neoadjuvant chemotherapy on response and survival in muscle-invasive bladder cancer. Methods NEOBLADE was a parallel-arm, double-blind, randomised, placebo-controlled, phase 2 trial of neoadjuvant gemcitabine and cisplatin chemotherapy with nintedanib or placebo in locally advanced muscle-invasive bladder cancer. Patients aged 18 years or older, with an Eastern Cooperative Oncology Group performance status of 0–1, were recruited from 15 hospitals in the UK. Patients were randomly assigned (1:1) to nintedanib or placebo using permuted blocks with random block sizes of two or four, stratified by centre and glomerular filtration rate. Treatments were allocated using an interactive web-based system, and patients and investigators were masked to treatment allocation throughout the study. Patients received oral nintedanib (150 mg or 200 mg twice daily for 12 weeks) or placebo, in addition to usual neoadjuvant chemotherapy with intravenous gemcitabine 1000 mg/m2 on days 1 and 8 and intravenous cisplatin 70 mg/m2 on day 1 of a 3-weekly cycle. The primary endpoint was pathological complete response rate, assessed at cystectomy or at day 8 of cycle 3 (plus or minus 7 days) if cystectomy did not occur. Primary analyses were done in the intention-to-treat population. The trial is registered with EudraCT, 2012-004895-01, and ISRCTN, 56349930, and has completed planned recruitment. Findings Between Dec 4, 2014, and Sept 3, 2018, 120 patients were recruited and were randomly allocated to receive nintedanib (n=57) or placebo (n=63). The median follow-up for the study was 33·5 months (IQR 14·0–44·0). Pathological complete response in the intention-to-treat population was reached in 21 (37%) of 57 patients in the nintedanib group and 20 (32%) of 63 in the placebo group (odds ratio [OR] 1·25, 70% CI 0·84–1·87; p=0·28). Grade 3 or worse toxicities were observed in 53 (93%) of 57 participants who received nintedanib and 50 (79%) of 63 patients in the placebo group (OR 1·65, 95% CI 0·74–3·65; p=0·24). The most common grade 3 or worse adverse events were thromboembolic events (17 [30%] of 57 patients in the nintedanib group vs 13 [21%] of 63 patients in the placebo group [OR 1·63, 95% CI 0·71–3·76; p=0·29]) and decreased neutrophil count (22 [39%] in the nintedanib group vs seven [11%] in the placebo group [5·03, 1·95–13·00; p=0·0006]). 45 treatment-related serious adverse events occurred in the nintedanib group and 43 occurred in the placebo group. One treatment-related death occurred in the placebo group, which was due to myocardial infarction. Interpretation The addition of nintedanib to chemotherapy was safe but did not improve the rate of pathological complete response in muscle-invasive bladder cancer