A polynomial version of Cereceda's conjecture

Let k and d be such that k ≥ d + 2. Consider two k-colourings of a d-degenerate graph G. Can we transform one into the other by recolouring one vertex at each step while maintaining a proper coloring at any step? Cereceda et al. answered that question in the affirmative, and exhibited a recolouring sequence of exponential length. However, Cereceda conjectured that there should exist one of quadratic length. The k-reconfiguration graph of G is the graph whose vertices are the proper k-colourings of G, with an edge between two colourings if they differ on exactly one vertex. Cereceda's conjecture can be reformulated as follows: the diameter of the (d + 2)-reconfiguration graph of any d-degenerate graph on n vertices is O(n 2). So far, the existence of a polynomial diameter is open even for d = 2. In this paper, we prove that the diameter of the k-reconfiguration graph of a d-degenerate graph is O(n d+1) for k ≥ d + 2. Moreover, we prove that if k ≥ 3 2 (d + 1) then the diameter of the k-reconfiguration graph is quadratic, improving the previous bound of k ≥ 2d + 1. We also show that the 5-reconfiguration graph of planar bipartite graphs has quadratic diameter, confirming Cereceda's conjecture for this class of graphs

Density functional perturbation theory within non-collinear magnetism

We extend the density functional perturbation theory formalism to the case of non-collinear magnetism. The main problem comes with the exchange-correlation (XC) potential derivatives, which are the only ones that are affected by the non-collinearity of the system. Most of the present XC functionals are constructed at the collinear level, such that the off-diagonal (containing magnetization densities along $x$ and $y$ directions) derivatives cannot be calculated simply in the non-collinear framework. To solve this problem, we consider here possibilities to transform the non-collinear XC derivatives to a local collinear basis, where the $z$ axis is aligned with the local magnetization at each point. The two methods we explore are i) expanding the spin rotation matrix as a Taylor series, ii) evaluating explicitly the XC for the local density approximation through an analytical expression of the expansion terms. We compare the two methods and describe their practical implementation. We show their application for atomic displacement and electric field perturbations at the second order, within the norm-conserving pseudopotential methods

Recoloring graphs of treewidth 2

Two (proper) colorings of a graph are adjacent if they differ on exactly one vertex. Jerrum proved that any $(d + 2)$-coloring of any d-degenerate graph can be transformed into any other via a sequence of adjacent colorings. A result of Bonamy et al. ensures that a shortest transformation can have a quadratic length even for $d = 1$. Bousquet and Perarnau proved that a linear transformation exists for between $(2d + 2)$-colorings. It is open to determine if this bound can be reduced. In this note, we prove that it can be reduced for graphs of treewidth 2, which are 2-degenerate. There exists a linear transformation between 5-colorings. It completes the picture for graphs of treewidth 2 since there exist graphs of treewidth 2 such a linear transformation between 4-colorings does not exist

Toward Optimal Run Racing: Application to Deep Learning Calibration

This paper aims at one-shot learning of deep neural nets, where a highly parallel setting is considered to address the algorithm calibration problem - selecting the best neural architecture and learning hyper-parameter values depending on the dataset at hand. The notoriously expensive calibration problem is optimally reduced by detecting and early stopping non-optimal runs. The theoretical contribution regards the optimality guarantees within the multiple hypothesis testing framework. Experimentations on the Cifar10, PTB and Wiki benchmarks demonstrate the relevance of the approach with a principled and consistent improvement on the state of the art with no extra hyper-parameter

Preventive fraction of physical fitness on risk factors in cardiac patients: Retrospective epidemiological study

International audienceAIM: To quantify the preventive fraction of physical fitness on the risk factors in patients with cardiovascular diseases (CVDs).METHODS: A total of 249 subjects (205 men and 44 women) suffering from CVD were categorized into four groups, according to their percentage of physical fitness. We calculated the odds ratio to obtain the preventive fraction in order to evaluate the impact of the physical fitness level on the risk factors (i.e. , abdominal obesity, depression, diabetes, dyslipidemia, hypertension, obesity, overweight and smoking).RESULTS: It is observed that a normal physical fitness level is sufficient to induce a preventive action on abdominal obesity (38%), diabetes (12%), hypertension (33%), obesity (12%) and overweight (11%). Also, the preventive fraction increases with the level of physical fitness, in particular for hypertension (36%) and overweight (16%). A high physical fitness level does not necessarily induce a preventive action in most risk factors, excluding depression.CONCLUSION: This is the first study which demonstrates that reaching a normal physical fitness level is enough to induce aprotection for some risk factors, despite having a CVD

Responsabilisation des conjoints aux comportements violents : regards des usagers des programmes

Les intervenants et les directeurs d’organismes d’aide aux conjoints aux comportements violents (CCV) du Québec et d’ailleurs s’entendent sur l’importance de responsabiliser ceux-ci. On peut toutefois se demander comment les hommes identifiés comme CCV réagissent à ce discours sur leur responsabilité. Cette recherche explore le discours de participants à des programmes d’aide sur la responsabilité, son évolution et ses points de convergence ou divergence avec le discours des intervenants et directeurs. La théorie de Loseke (2003) sur la construction des problèmes sociaux a été le cadre théorique retenu pour cette recherche. Les points de vue de 14 usagers de programmes situés dans trois régions différentes du Québec ont été recueillis dans le cadre de groupes de discussion focalisée et, exceptionnellement pour l’un des participants, dans le cadre d’un entretien individuel. De manière générale, les participants reconnaissent être responsables de leur violence. Toutefois, ils éprouvent de la difficulté à se percevoir comme des acteurs entièrement rationnels et à établir des frontières claires entre leur responsabilité et celle de leur partenaire. Ces résultats sont discutés et des recommandations sont formulées pour des recherches futures et les milieux de pratique.Practitioners and program managers in agencies for men perpetrators of intimatepartner violence (IPV) from Quebec and elsewhere agree about the significance of one’s responsibility. Nevertheless, one wonders how men identified as violent partners react to this discourse about their responsibility. This research seeks toexplore the discourse of participants attending IPV programs about responsibility, its evolution, and the ways in which it interacts with the practitioners and the programmanagers' discourses. Loseke's (2003) theory on the construction of social problemswas the theoretical framework chosen for this research. Fourteen men from three different areas in Quebec were met during focus groups and, exceptionally for one of the participants, through one individual interview. In general, participants recognize their responsibility within their violent behavior. However, they experienced difficulty seeing themselves as entirely rational agents and establishing clear limits between their responsibility and their partner's. The results of this research are discussed and recommendations are given for both further research and practical areas

Compressed sensing reconstruction of convolved sparse signals

Abstract—This paper addresses the problem of efficient sam-pling and reconstruction of sparse spike signals, which have been convolved with low-pass filters. A modified compressed sensing (CS) framework is proposed, termed dictionary-based deconvolution CS (DDCS) to achieve this goal. DDCS builds on the assumption that a low-pass filter can be represented sparsely in a dictionary of blurring atoms. Identification of both the sparse spike signal and the sparsely parameterized blurring function is performed by an alternating scheme that minimizes each variable independently, while keeping the other constant. Simulation results reveal that the proposed DDSS scheme achieves an improved reconstruction performance when compared to traditional CS recovery. I

PACE Solver Description: ?Solver - Heuristic Track

This document describes our heuristic Cluster Editing solver, ?Solver, which got the third place in the 2021 PACE Challenge. We present the local search and kernelization techniques for Cluster Editing that are implemented in the solver