The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs

The packing chromatic number χ_{p}(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,...,Vk , where vertices in Vi have pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes._{}

Vanishing Contagion Spreads

We study default in a multifirm equilibrium setting with incomplete information. Defaults are consistent with the firm’s balance sheet and aggregation. We show that the endogenous volatility and jump size of debt and equity generated by other firms’ shocks vanish as the number of firms in the economy increases. As a result, credit spreads depend asymptotically only on the firms’ own cash flow risk. Our vanishing contagion spread result calls into question recent findings based on production economies, in which quantities of risk (volatilities and jump sizes of securities) are specified exogenously, that attribute credit spreads mostly to contagion. This paper was accepted by Kay Giesecke, finance.

STOCHASTIC VOLATILITY MODEL WITH CORRELATED JUMP SIZES AND INDEPENDENT ARRIVALS

In light of recent empirical research on jump activity, this article study the calibration of a new class of stochastic volatility models that include both jumps in return and volatility. Specifically, we consider correlated jump sizes and both contemporaneous and independent arrival of jumps in return and volatility. Based on the specifications of this model, we derive a closed-form relationship between the VIX index and latent volatility. Also, we propose a closed-form logarithmic likelihood formula by using the link to the VIX index. By estimating alternative models, we find that the general counting processes setting lead to better capturing of return jump behaviors. That is, the part where the return and volatility jump simultaneously and the part that jump independently can both be captured. In addition, the size of the jumps in volatility is, on average, positive for both contemporaneous and independent arrivals. However, contemporaneous jumps in the return are negative, but independent return jumps are positive. The sub-period analysis further supports above insight, and we find that the jumps in return and volatility increased significantly during the two recent economic crises.

Cоотношение Холла-Петча для размеров скачков деформации металлов

The paper presents an attempt to use the Hall–Petch relationship to relate the yield strength of copper and titanium in three different states (initial, annealed, and after equal-channel angular pressing) to the sizes of nano- and micrometer deformation jumps measured using a precision interferometric technique. It is shown that, upon a compression strain near the yield point, one can observe six levels of deformation with three nano- and three micrometer sizes of deformation jumps from 1–2 nm to 20–35 μm. Each of the six structural states of metals is characterized by its own set of deformation jump sizes. Dependences of the yield strengths of copper and titanium on the jump sizes L ^–1/2 are constructed, and the general regularities and features of deformation jumps for each of the metals in different structural states are discussed.

The Unrestricted Black-Box Complexity of Jump Functions

We analyze the unrestricted black-box complexity of the Jump function classes for different jump sizes. For upper bounds, we present three algorithms for small, medium, and extreme jump sizes. We prove a matrix lower bound theorem which is capable of giving better lower bounds than the classic information theory approach. Using this theorem, we prove lower bounds that almost match the upper bounds. For the case of extreme jump functions, which apart from the optimum reveal only the middle fitness value(s), we use an additional lower bound argument to show that any black-box algorithm does not gain significant insight about the problem instance from the first [Formula: see text] fitness evaluations. This, together with our upper bound, shows that the black-box complexity of extreme jump functions is [Formula: see text].