Pozicione igre na grafovima

\section*{Abstract} We study Maker-Breaker games played on the edges of the complete graph on $n$ vertices, $K_n$, whose family of winning sets \cF consists of all edge sets of subgraphs $G\subseteq K_n$ which possess a predetermined monotone increasing property. Two players, Maker and Breaker, take turns in claiming $a$, respectively $b$, unclaimed edges per move. We are interested in finding the threshold bias b_{\cF}(a) for all values of $a$, so that for every $b$, b\leq b_{\cF}(a), Maker wins the game and for all values of $b$, such that b>b_{\cF}(a), Breaker wins the game. We are particularly interested in cases where both $a$ and $b$ can be greater than $1$. We focus on the \textit{Connectivity game}, where the winning sets are the edge sets of all spanning trees of $K_n$ and on the  \textit{Hamiltonicity game}, where the winning sets are the edge sets of all Hamilton cycles on $K_n$. Next, we consider biased $(1:b)$ Avoider-Enforcer games, also played on the edges of $K_n$. For every constant $k\geq 3$ we analyse the $k$-star game, where Avoider tries to avoid claiming $k$ edges incident to the same vertex. We analyse both versions of Avoider-Enforcer games, the strict and the monotone, and for each provide explicit winning strategies for both players. Consequentially, we establish bounds on the threshold biases f^{mon}_\cF, f^-_\cF and f^+_\cF, where \cF is the hypergraph of the game (the family of target sets). We also study the monotone version of $K_{2,2}$-game, where Avoider wants to avoid claiming all the edges of some graph isomorphic to $K_{2,2}$ in $K_n$.   Finally, we search for the fast winning strategies for Maker in Perfect matching game and Hamiltonicity game, again played on the edge set of $K_n$. Here, we look at the biased $(1:b)$ games, where Maker's bias is 1, and Breaker's bias is $b, b\ge 1$.\section*{Izvod} Prou\v{c}avamo takozvane Mejker-Brejker (Maker-Breaker) igre koje se igraju na granama kompletnog grafa sa $n$ \v{c}vorova, $K_n$, \v{c}ija familija pobedni\v{c}kih skupova \cF obuhvata sve skupove grana grafa $G\subseteq K_n$ koji imaju neku monotono rastu\'{c}u osobinu. Dva igra\v{c}a, \textit{Mejker} (\textit{Pravi\v{s}a}) i \textit{Brejker} (\textit{Kva\-ri\-\v{s}a}) se smenjuju u odabiru $a$, odnosno $b$, slobodnih grana po potezu. Interesuje nas da prona\dj emo grani\v{c}ni bias b_{\cF}(a) za sve vrednosti pa\-ra\-me\-tra $a$, tako da za svako $b$, b\le b_{\cF}(a), Mejker pobe\dj uje u igri, a za svako $b$, takvo da je b>b_{\cF}(a), Brejker pobe\dj uje. Posebno nas interesuju slu\v{c}ajevi u kojima oba parametra $a$ i $b$ mogu imati vrednost ve\'cu od 1. Na\v{s}a pa\v{z}nja je posve\'{c}ena igri povezanosti, gde su pobedni\v{c}ki skupovi  grane svih pokrivaju\'cih stabala grafa $K_n$, kao i igri Hamiltonove konture, gde su pobedni\v{c}ki skupovi grane svih Hamiltonovih kontura grafa $K_n$. Zatim posmatramo igre tipa Avojder-Enforser (Avoider-Enforcer), sa biasom $(1:b)$, koje se tako\dj e igraju na granama kompletnog grafa sa $n$ \v{c}vorova, $K_n$. Za svaku konstantu $k$, $k\ge 3$ analiziramo igru $k$-zvezde (zvezde sa $k$ krakova), u kojoj \textit{Avojder} poku\v{s}va da izbegne da ima $k$ svojih grana incidentnih sa istim \v{c}vorom. Posmatramo obe verzije ove igre, striktnu i monotonu, i za svaku dajemo eksplicitnu pobedni\v{c}ku strategiju za oba igra\v{c}a. Kao rezultat, dobijamo gornje i donje ograni\v{c}enje za grani\v{c}ne biase f^{mon}_\cF, f^-_\cF i f^+_\cF, gde \cF predstavlja hipergraf igre (familija ciljnih skupova). %$f^{mon}$, $f^-$ and $f^+$. Tako\dj e, posmatramo i monotonu verziju $K_{2,2}$-igre, gde Avojder \v{z}eli da izbegne da graf koji \v{c}ine njegove grane sadr\v{z}i graf izomorfan sa $K_{2,2}$. Kona\v{c}no, \v{z}elimo da prona\dj emo strategije za brzu pobedu Mejkera u igrama savr\v{s}enog me\v{c}inga i Hamiltonove konture, koje se tako\dj e igraju na granama kompletnog grafa $K_n$. Ovde posmatramo asimetri\v{c}ne igre gde je bias Mejkera 1, a bias Brejkera $b$, $b\ge 1$

A Cooperation Infrastructure For Communication Between Public Bodies; The Friuli Venezia Giulia Case

Long ago, Italian Public Administrations started a process to increase the efficiency of their administrative procedures, adopting ICT technologies and tools in place of paperwork, but the approach was not structured nor synchronized. The result now is that Public Authorities’ legacy systems are based upon heterogeneous and vendor specific solutions. To increase their efficiency is one of the most challenging issues that Public Administrations are facing in the latest years in order to ensure a faster communication among public bodies, avoid data redundancy and improve the service provided to citizens. The key element is to increase the cooperation among public bodies allowing a seamless communication which will not modify the already existing systems. The Friuli Venezia Giulia Region interoperability framework, presented in this paper, provides a layer which ensure the communication between Administrations increasing the efficiency of administrative procedures, through the adoption of secure electronic communication, and lead to the delivery of a better public service in terms of content and response tim

Exact Top Yukawa corrections to Higgs boson decay into bottom quarks

In this letter we present the results of the exact computation of contributions to the Higgs boson decay into bottom quarks that are proportional to the top Yukawa coupling. Our computation demonstrates that approximate results already available in the literature turn out to be particularly accurate for the three physical mass values of the Higgs boson, the bottom and top quarks. Furthermore, contrary to expectations, the impact of these corrections on differential distributions relevant for the searches of the Higgs boson decaying into bottom quarks at the Large Hadron Collider is rather small.Comment: 6 pages, 4 figure

Randomized Constraints Consensus for Distributed Robust Mixed-Integer Programming

In this paper, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under asynchronous, unreliable and directed communication. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: (i) a verification in which they check---in a randomized fashion---the robust feasibility of a candidate optimal point, and (ii) an optimization step in which they exchange their candidate basis (the minimal set of constraints defining a solution) with neighbors and locally solve an optimization problem. As main result, we show that processors can stop the algorithm after a finite number of communication rounds (either because verification has been successful for a sufficient number of rounds or because a given threshold has been reached), so that candidate optimal solutions are consensual. The common solution is proven to be---with high confidence---feasible and hence optimal for the entire set of uncertainty except a subset having an arbitrary small probability measure. We show the effectiveness of the proposed distributed algorithm using two examples: a random, uncertain mixed-integer linear program and a distributed localization in wireless sensor networks. The distributed algorithm is implemented on a multi-core platform in which the nodes communicate asynchronously.Comment: Submitted for publication. arXiv admin note: text overlap with arXiv:1706.0048

Bipolar Patients and Bullous Pemphigoid after Risperidone Long-Acting Injectable: A Case Report and a Review of the Literature

Neuropsychiatric disorders are found to be associated with bullous pemphigoid (BP), an autoimmune subepidermal blistering disease. Antipsychotics have emerged as possible inducing factors of BP. However, large sample studies concerning BP associated with antipsychotics, as well as with specific mental disorders, are still lacking. Our review retrieved a few clinical studies and case reports on the topic, producing controversial results. We report for the first time a bipolar patient case presenting BP following five-month therapy with risperidone long-acting injectable (LAI). We hypothesize that the dermatological event is associated with the medication administered. The issue emerged during psychiatric consultation and was confirmed by histological examination, direct and indirect immunofluorescence studies, plus positive plasma and cutaneous BP180 and BP230 IgG. Neurodegeneration or neuroinflammation might represent a primary process leading to a cross-reactive immune response between neural and cutaneous antigens and contributing to self-tolerance failure. Furthermore, the time sequence of the shared biological mechanisms leading to clinical manifestations of the neuropsychiatric disorder and BP remains undefined. BP comorbid with bipolar disorder might occasionally represent a serious health risk and affect patients’ physical and psychosocial quality of life. Thus, clinicians treating psychiatric patients should consider BP as a possible adverse effect of psychotropic medications

selection of solar collectors technology and surface for a desiccant cooling system based on energy environmental and economic analysis

Desiccant-based air handling units allow significant reductions in greenhouse gas emissions and energy savings with respect to conventional air conditioning systems. Benefits are maximized when they interact with renewable energy technologies, such as solar collectors. Due to the high requirements of humidifiers, water consumption is a major issue for desiccant cooling technology. Therefore, a water consumption analysis should be also performed.In this work, experimental tests and data derived from scientific and technical literature are used to implement a model of a solar desiccant cooling system, considering three different solar caption technologies (air, flat plate and evacuated collectors). Simulations were then performed to compare the energy, environmental and economic performance and water consumption of the system with those of a desiccant-based unit in which regeneration thermal energy is supplied by a natural gas boiler, and with a conventional air handling device. A trade-off solution is chosen, consisting of 16 m2 of flat-plate solar collectors. This solution allows to obtain, with respect to the reference system, a reduction of primary energy consumption and of the equivalent CO2 emissions of 24.2% and 27.1%, respectively, with an acceptable pay-back time of 4.81 years, and a water consumption very similar to that of the reference system

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We have reviewed the impact of the ubiquitin proteasome system (UPS) on atherosclerosis progression of diabetic patients. A puzzle of many pieces of evidence suggests that UPS, in addition to its role in the removal of damaged proteins, is involved in a number of biological processes including inflammation, proliferation and apoptosis, all of which constitute important characteristics of atherosclerosis. From what can be gathered from the very few studies on the UPS in diabetic cardiovascular diseases published so far, the system seems to be functionally active to a different extent in the initiation, progression, and complication stage of atherosclerosis in the diabetic people. Further evidence for this theory, however, has to be given, for instance by specifically targeted antagonism of the UPS. Nonetheless, this hypothesis may help us understand why diverse therapeutic interventions, which have in common the ability to reduce ubiquitin-proteasome activity, can impede or delay the onset of diabetes and cardiovascular diseases (CVD)