Liquidation Triggers and the Valuation of Equity and Debt

Net-worth covenants, as introduced by Black and Cox (1976), provide the firm’s bondholders with the right to force reorganization or liquidation if the value of the firm falls below a certain threshold. In the event of default, however, many bankruptcy codes stipulate an automatic stay of assets that prevent bondholders from triggering liquidation and thus impact many positive net-worth covenants. To consider this impact on a corporation’s capital structure we develop a general model of liquidation driven by a liquidation trigger. This trigger accumulates with time and severity of distress. In addition, current distress periods may have greater weight than old ones. The tractability of the approach stems from its ability to allow parameters appropriate for different legal rules and types of bondholder safety covenants. The proposed model includes several well-known models, like Merton, Black- Cox and others. We show how to valuate various types of corporate securities by using this model. Numerical results and sensitivity analysis are presented for selected basic cases.default, bankruptcy, liquidation trigger, debt pricing, corporate finance

Ramsey-nice families of graphs

For a finite family $\mathcal{F}$ of fixed graphs let $R_k(\mathcal{F})$ be the smallest integer $n$ for which every $k$-coloring of the edges of the complete graph $K_n$ yields a monochromatic copy of some $F\in\mathcal{F}$. We say that $\mathcal{F}$ is $k$-nice if for every graph $G$ with $\chi(G)=R_k(\mathcal{F})$ and for every $k$-coloring of $E(G)$ there exists a monochromatic copy of some $F\in\mathcal{F}$. It is easy to see that if $\mathcal{F}$ contains no forest, then it is not $k$-nice for any $k$. It seems plausible to conjecture that a (weak) converse holds, namely, for any finite family of graphs $\mathcal{F}$ that contains at least one forest, and for all $k\geq k_0(\mathcal{F})$ (or at least for infinitely many values of $k$), $\mathcal{F}$ is $k$-nice. We prove several (modest) results in support of this conjecture, showing, in particular, that it holds for each of the three families consisting of two connected graphs with 3 edges each and observing that it holds for any family $\mathcal{F}$ containing a forest with at most 2 edges. We also study some related problems and disprove a conjecture by Aharoni, Charbit and Howard regarding the size of matchings in regular 3-partite 3-uniform hypergraphs.Comment: 20 pages, 2 figure

Cytokine response to typical field sports practices in adolescent athletes

The present study compares previous reports on the effect of “real-life” typical field individual (i.e. cross country running and wrestling – representing combat versus non-combat sports) and team sports (i.e. volleyball and water-polo – representing water and land team sports) training on pro (IL-6) and anti (IL-1 receptor antagonist – IL-1ra) inflammatory mediators in male and female late pubertal athletes. An increase in IL-6 was found following each of the training sessions. In contrast, a significant increase in IL-1ra was found only following the cross-country, wrestling and water-polo practices and not following the volleyball practices in both genders. There was no difference in the inflammatory response between individual and team sports practices. The inflammatory response to the typical practices was correlated with the practice-associated lactate change. The greatest increase in IL-6 and IL-1ra occurred following contact sport practices, and was greater following land (wrestling) compared to the water (water-polo) practice suggesting that this increase may reflect muscle tissue damage and not necessarily training intensity. Further research is needed to better understand the influence of “real-life” typical training on exercise training adaptations of adolescent athletes

Repeated sprint test performance indices and aerobic fitness in normal and overweight pre-pubertal children

We determined relationships between aerobic fitness and performance indices (fastest sprint time – FS, total sprint time – TS, and performance decrement – PD) of repeated sprint tests (RST) in normal and overweight children (BMI%: 59.8±12.9 versus 96.4±1.9%, respectively). Aerobic fitness, FS, and TS were significantly higher in normal weight children. Significant negative correlations were found between aerobic fitness and TS (r=–0.802), FS (r=–0.762) and PD (r=–0.670) in normal weight children. Significant negative correlations between aerobic fitness and TS (r=–0.767) and FS (r=–0.738), but not with PD were found in overweight children. While aerobic and anaerobic capabilities were significantly higher in normal weight children, strong relationships were found between aerobic fitness and RST indices in both normal and overweight children

The effect of methylphenidate treatment on exercise performance in children with attention-deficit hyperactivity disorder

The prevalence of attention-deficit hyperactivity disorder (ADHD) in the school-age population is 8–10%, with boys having higher prevalence than girls. Children with ADHD have reduced physical fitness characteristics and exercise capacity compared to healthy children. There are conflicting results regarding the effect of treatment on exercise performance in children with ADHD. We determined fitness characteristic in children with ADHD receiving methylphenidate treatment (17.5±0.6 years; n=16) compared to age-adjusted ADHD children not receiving treatment (17.2±0.7 years; n=16). There were no significant differences in anthropometric measures between the treated and non-treated participants. There were no significant differences in the 60 seconds sit ups number, number of pull-ups, 4X10m shuttle run times and 2000m running times between the treated and non-treated participants. Standing long-jump results were significantly better among the non-treated ADHD participants (p<0.02). The results suggest that methylphenidate treatment might be disadvantageous for maximal speed and explosive-type activities in ADHD patient. Further studies are needed to clarify if other sports activities which require attention, accuracy, concentration and organization may benefit from such treatment

Playing to Retain the Advantage

Let P be a monotone increasing graph property, let G = (V, E) be a graph, and let q be a positive integer. In this paper, we study the (1: q) Maker-Breaker game, played on the edges of G, in which Maker's goal is to build a graph that satisfies the property P. It is clear that in order for Maker to have a chance of winning, G itself must satisfy P. We prove that if G satisfies P in some strong sense, that is, if one has to delete sufficiently many edges from G in order to obtain a graph that does not satisfy P, then Maker has a winning strategy for this game. We also consider a different notion of satisfying some property in a strong sense, which is motivated by a problem of Duffus, Łuczak and Rödl [6

Health-related knowledge and preferences in low socio-economic kindergarteners

<p>Abstract</p> <p>Objective</p> <p>The aim of the present study was to determine physical activity (PA) and nutrition knowledge and preferences in low socio-economic status kindergarten children.</p> <p>Methods</p> <p>Following height and weight measurement, 795 low socio-economic status kindergarten children (age 3.8-6.8 y.o) completed a photo-pair knowledge and preferences food and exercise questionnaire.</p> <p>Results</p> <p>No difference was found between nutrition and PA knowledge scores (52.3 ± 0.9 versus 52.6 ± 0.8%, respectively). There was no difference between the nutrition knowledge and preference score (52.3 ± 0.9 versus 50.9 ± 0.9%, respectively). PA preference was significantly higher than knowledge (56.9 ± 1.5 versus 52.6 ± 0.8%, respectively; p < 0.0001). Significant correlations were found between nutrition knowledge and preferences (r = 0.55, p < 0.0001), physical activity knowledge and preferences (r = 0.46, p < 0.0001), and nutrition and PA preferences (r = 0.46, p < 0.001). Nutrition preference scores were significantly lower in overweight compared to normal weight kindergartners 48.1 ± 1.7 versus 52.0 ± 1.0%; p < 0.05). PA knowledge and preference scores were significantly higher among male compared to the female kindergartners (p < 0.001 for both).</p> <p>Conclusion</p> <p>Our data demonstrate diversities in physical activity and nutrition knowledge and preferences among low socio-economic status kindergarten children. These findings may be important for the development of health promotion programs in low socioeconomic kindergarten children.</p

Edge-statistics on large graphs

The inducibility of a graph $H$ measures the maximum number of induced copies of $H$ a large graph $G$ can have. Generalizing this notion, we study how many induced subgraphs of fixed order $k$ and size $\ell$ a large graph $G$ on $n$ vertices can have. Clearly, this number is $\binom{n}{k}$ for every $n$, $k$ and $\ell \in \left \{0, \binom{k}{2} \right\}$. We conjecture that for every $n$, $k$ and $0 < \ell < \binom{k}{2}$ this number is at most $\left(1/e + o_k(1) \right) \binom{n}{k}$. If true, this would be tight for $\ell \in \{1, k-1\}$. In support of our `Edge-statistics conjecture' we prove that the corresponding density is bounded away from $1$ by an absolute constant. Furthermore, for various ranges of the values of $\ell$ we establish stronger bounds. In particular, we prove that for `almost all' pairs $(k, \ell)$ only a polynomially small fraction of the $k$-subsets of $V(G)$ has exactly $\ell$ edges, and prove an upper bound of $(1/2 + o_k(1))\binom{n}{k}$ for $\ell = 1$. Our proof methods involve probabilistic tools, such as anti-concentration results relying on fourth moment estimates and Brun's sieve, as well as graph-theoretic and combinatorial arguments such as Zykov's symmetrization, Sperner's theorem and various counting techniques.Comment: 23 pages, revised versio