{Improved Bounds on Fourier Entropy and Min-entropy}

Given a Boolean function $f:\{-1,1\}^n\to \{-1,1\}$, the Fourier distribution assigns probability $\widehat{f}(S)^2$ to $S\subseteq [n]$. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai asks if there exist a universal constant C>0 such that $H(\hat{f}^2)\leq C Inf(f)$, where $H(\hat{f}^2)$ is the Shannon entropy of the Fourier distribution of $f$ and $Inf(f)$ is the total influence of $f$. 1) We consider the weaker Fourier Min-entropy-Influence (FMEI) conjecture. This asks if $H_{\infty}(\hat{f}^2)\leq C Inf(f)$, where $H_{\infty}(\hat{f}^2)$ is the min-entropy of the Fourier distribution. We show $H_{\infty}(\hat{f}^2)\leq 2C_{\min}^\oplus(f)$, where $C_{\min}^\oplus(f)$ is the minimum parity certificate complexity of $f$. We also show that for every $\epsilon\geq 0$, we have $H_{\infty}(\hat{f}^2)\leq 2\log (\|\hat{f}\|_{1,\epsilon}/(1-\epsilon))$, where $\|\hat{f}\|_{1,\epsilon}$ is the approximate spectral norm of $f$. As a corollary, we verify the FMEI conjecture for the class of read-$k$ $DNF$s (for constant $k$). 2) We show that $H(\hat{f}^2)\leq 2 aUC^\oplus(f)$, where $aUC^\oplus(f)$ is the average unambiguous parity certificate complexity of $f$. This improves upon Chakraborty et al. An important consequence of the FEI conjecture is the long-standing Mansour's conjecture. We show that a weaker version of FEI already implies Mansour's conjecture: is $H(\hat{f}^2)\leq C \min\{C^0(f),C^1(f)\}$?, where $C^0(f), C^1(f)$ are the 0- and 1-certificate complexities of $f$, respectively. 3) We study what FEI implies about the structure of polynomials that 1/3-approximate a Boolean function. We pose a conjecture (which is implied by FEI): no "flat" degree-$d$ polynomial of sparsity $2^{\omega(d)}$ can 1/3-approximate a Boolean function. We prove this conjecture unconditionally for a particular class of polynomials

Anonymous Graph Exploration with Binoculars

International audienceWe investigate the exploration of networks by a mobile agent. It is long known that, without global information about the graph, it is not possible to make the agent halts after the exploration except if the graph is a tree. We therefore endow the agent with binoculars, a sensing device that can show the local structure of the environment at a constant distance of the agent current location.We show that, with binoculars, it is possible to explore and halt in a large class of non-tree networks. We give a complete characterization of the class of networks that can be explored using binoculars using standard notions of discrete topology. This class is much larger than the class of trees: it contains in particular chordal graphs, plane triangulations and triangulations of the projective plane. Our characterization is constructive, we present an Exploration algorithm that is universal; this algorithm explores any network explorable with binoculars, and never halts in non-explorable networks

Actual changes in system of urban planning in post-socialist city: the case of Prague

After the change of political system in Czechoslovakia (1989) came also a lot of social, economical and cultural changes. Today, all the Czech cities stay in front of the biggest change of city planning philosophy in last two decades. Prague, the capital city of Czech Republic, decided for a big institutional transition in 2012. The municipality, in cooperation with Faculty of Architecture CTU in Prague, is preparing completely pioneering methodology for quality commissioning of land use plans and, in cooperation with the new Institute of Planning and Development, is preparing innovative system of city planning. There are new ordinances, laws, regulations, tourist trade strategies and many other documents. Prague, as one of the strongest regions in East-Central Europe, can be seen like a laboratory of current development of post-socialist city. The new methodology of Metropolitan Plan could be a key to success

Laboratory rotational spectroscopy of acrylamide and a search for acrylamide and propionamide toward Sgr B2(N) with ALMA

Context. Numerous complex organic molecules have been detected in the universe and among them are amides, which are considered as prime models for species containing a peptide linkage. In its backbone, acrylamide (CH2CHC(O)NH2) bears not only the peptide bond, but also the vinyl functional group that is a common structural feature in many interstellar compounds. This makes acrylamide an interesting candidate for searches in the interstellar medium. In addition, a tentative detection of the related molecule propionamide (C2H5C(O)NH2) has been recently claimed toward Sgr B2(N). Aims. The aim of this work is to extend the knowledge of the laboratory rotational spectrum of acrylamide to higher frequencies, which would make it possible to conduct a rigorous search for interstellar signatures of this amide using millimeter wave astronomy. Methods. We measured and analyzed the rotational spectrum of acrylamide between 75 and 480 GHz. We searched for emission of acrylamide in the imaging spectral line survey ReMoCA performed with the Atacama Large Millimeter/submillimeter Array toward Sgr B2(N). We also searched for propionamide in the same source. The astronomical spectra were analyzed under the assumption of local thermodynamic equilibrium. Results. We report accurate laboratory measurements and analyses of thousands of rotational transitions in the ground state and two excited vibrational states of the most stable syn form of acrylamide. In addition, we report an extensive set of rotational transitions for the less stable skew conformer. Tunneling through a low energy barrier between two symmetrically equivalent configurations has been revealed for this higher-energy species. Neither acrylamide nor propionamide were detected toward the two main hot molecular cores of Sgr B2(N). We did not detect propionamide either toward a position located to the east of the main hot core, thereby undermining the recent claim of its interstellar detection toward this position. We find that acrylamide and propionamide are at least 26 and 14 times less abundant, respectively, than acetamide toward the main hot core Sgr B2(N1S), and at least 6 and 3 times less abundant, respectively, than acetamide toward the secondary hot core Sgr B2(N2). Conclusions. A comparison with results of astrochemical kinetics model for related species suggests that acrylamide may be a few hundred times less abundant than acetamide, corresponding to a value that is at least an order of magnitude lower than the observational upper limits. Propionamide may be as little as only a factor of two less abundant than the upper limit derived toward Sgr B2(N1S). Lastly, the spectroscopic data presented in this work will aid future searches of acrylamide in space

Organizational and Sociodemographic Determinants of Job Satisfaction in the Czech Republic

This study examines the effect of personal and work-related factors on job satisfaction based on a sample from the Czech Republic. The study, which was based on a questionnaire survey of 1,776 respondents in organizations in the Czech Republic, proposed a number of hypotheses related to demographic and organizational variables and tests using ANOVA. Results of the data analysis revealed similarities to findings in Western countries, in which men show higher job satisfaction than women. Age does not seem to have a significant effect on job satisfaction. There is low job satisfaction in public/governmental organizations and among young people entering the job market. It is suggested that it is necessary to develop a human resources strategy for the public/governmental sector that will not only increase its social prestige but also increase positive feelings among its employees. The need to better prepare undergraduates for the demands of the job market is also discussed