Efficient multithreaded untransposed,transposed or symmetric sparse matrix–vector multiplication with the Recursive Sparse Blocks format

In earlier work we have introduced the “Recursive Sparse Blocks” (RSB) sparse matrix storage scheme oriented towards cache efficient matrix–vector multiplication (SpMV) and triangular solution (SpSV) on cache based shared memory parallel computers. Both the transposed (SpMV_T) and symmetric (SymSpMV) matrix–vector multiply variants are supported. RSB stands for a meta-format: it recursively partitions a rectangular sparse matrix in quadrants; leaf submatrices are stored in an appropriate traditional format — either Compressed Sparse Rows (CSR) or Coordinate (COO). In this work, we compare the performance of our RSB implementation of SpMV, SpMV_T, SymSpMV to that of the state-of-the-art Intel Math Kernel Library (MKL) CSR implementation on the recent Intel’s Sandy Bridge processor. Our results with a few dozens of real world large matrices suggest the efficiency of the approach: in all of the cases, RSB’s SymSpMV (and in most cases, SpMV_T as well) took less than half of MKL CSR’s time; SpMV’s advantage was smaller. Furthermore, RSB’s SpMV_T is more scalable than MKL’s CSR, in that it performs almost as well as SpMV. Additionally, we include comparisons to the state-of-the art format Compressed Sparse Blocks (CSB) implementation. We observed RSB to be slightly superior to CSB in SpMV_T, slightly inferior in SpMV, and better (in most cases by a factor of two or more) in SymSpMV. Although RSB is a non-traditional storage format and thus needs a special constructor, it can be assembled from CSR or any other similar row-ordered representation arrays in the time of a few dozens of matrix–vector multiply executions. Thanks to its significant advantage over MKL’s CSR routines for symmetric or transposed matrix–vector multiplication, in most of the observed cases the assembly cost has been observed to amortize with fewer than fifty iterations.     

Funding and investment decisions in a stochastic defined benefit pension plan with several levels of labor-income earnings

In this paper we consider the optimal management of an aggregated dynamic pension fund. There are n$n$ classes of workers whose salaries are stochastic. A portion of the salary is contributed to the funding process and the manager invests in a portfolio with m$m$ risky assets and a risk-free security. The main objective is to minimize the cost of contributions in a bounded horizon T$T$ and to maximize the utility of final surplus, measured as the relative fund level respect to the mean salary. The aim of the paper is to describe the properties of fund allocation and optimal contribution when salaries differ across contributors to the fund.     

Existence of solutions to singular integral equations

Nonnegative solutions are established for singular integral equations of the form y(t) = h(t) + ∫^T₀ k(t, s)f(s, y(s)) ds for t ∈ [0, T]. Here f may be singular at y = 0.     

High-Water Marks and Hedge Fund Management Contracts with Partial Information

This paper extends the Goetzmann et al. (J Financ 58:1685–1717, 2003) model to the case of partial information, where the expected return of a hedge fund is not observable but known to be either high or low. The fund manager can dynamically update his belief about the true value of the expected return based on the realization of the net asset value of the hedge fund. Our main purpose is to study the impact of the uncertainty of the expected return on the pricing of the fund manager’s various fees and the investor’s claim. The results show that partial information has significant impact on the values of the fees and the claim. Specifically, a non-updating fund manager always underestimate the values, and more often than not, the amount underestimated is very significant. The closer the net asset value gets to the high-water mark or the larger the uncertainty of the expected return is, the bigger the amount underestimated will become.     

A class of non-zero-sum stochastic differential investment and reinsurance games

In this article, we provide a systematic study on the non-zero-sum stochastic differential investment and reinsurance game between two insurance companies. Each insurance company’s surplus process consists of a proportional reinsurance protection and an investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer–Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound economic interpretations, for the case of an exponential utility function.     

Periodic input estimation for linear periodic systems: Automotive engine applications

In this paper, we consider periodic linear systems driven by T₀-periodic signals that we desire to reconstruct. The systems under consideration are of the form , y=C(t)x, x∈Rⁿ, w∈R^m, y∈R^p, (m?p?n) where A(t), A₀(t), and C(t) are T₀-periodic matrices. The period T₀ is known. The T₀-periodic input signal w(t) is unknown but is assumed to admit a finite dimensional Fourier decomposition. Our contribution is a technique to estimate w from the measurements y. In both full state measurement and partial state measurement cases, we propose an efficient observer for the coefficients of the Fourier decomposition of w(t). The proposed techniques are particularly attractive for automotive engine applications where sampling time is short. In this situation, standard estimation techniques based on Kalman filters are often discarded (because of their relative high computational burden). Relevance of our approach is supported by two practical cases of application. Detailed convergence analysis is also provided. Under standard observability conditions, we prove asymptotic convergence when the tuning parameters are chosen sufficiently small.     

The elements of probabilistic time geography

Time geography uses space–time volumes to represent the possible locations of a mobile agent over time in a x–y–t space. A volume is a qualitative representation of the fact that the agent is at a particular time t _i inside of the volume’s base at t _i . Space–time volumes enable qualitative analysis such as potential encounters between agents. In this paper the qualitative statements of time geography will be quantified. For this purpose an agent’s possible locations are modeled from a stochastic perspective. It is shown that probability is not equally distributed in a space–time volume, i.e., a quantitative analysis cannot be based simply on proportions of intersections. The actual probability distribution depends on the degree of a priori knowledge about the agent’s behavior. This paper starts with the standard assumption of time geography (no further knowledge), and develops the appropriate probability distribution by three equivalent approaches. With such a model any analysis of the location of an agent, or relations between the locations of two agents, can be improved in expressiveness as well as accuracy.     

Blackwell’s Theorem for T-related fuzzy variables

In this paper, we consider Blackwell’s Theorem in which inter-arrival times are characterized as fuzzy variables under t-norm-based fuzzy operations. We first prove that Blackwell’s Theorem for T-related fuzzy variables with respect to necessity measure holds true where T is an Archimedean t-norm. Subsequently, we provide a counter example under which Blackwell’s Theorem does not hold when T = min. Finally, we evaluate the expected value of fuzzy variable with respect to credibility measure and derive fuzzy Blackwell’s Theorem based on the expected value of fuzzy variables.     

Generating effective defined-contribution pension plan using simulation optimization approach

This paper presents an optimization approach to analyze the problems of portfolio selection for long-term investments, taking into consideration the specific target replacement ratio for defined-contribution (DC) pension scheme; the purpose is to generate an effective multi-period asset allocation that reaches an amount matching the target liability at retirement date and reduce the downside risk of the investment. A multi-period asset liability simulation model was used to generate 4000 asset return predictions, and an evolutionary algorithm, evolution strategies, was incorporated into the model to generate multi-period asset allocations under four conditions, considering different weights for measuring the importance of matching the target liability and different periods of downside risk measurement. Computational results showed that the evolutionary algorithm, evolution strategies, is a very robust and effective approach to generate promising asset allocations under all the four cases. In addition, computational results showed that the promising asset allocations revealed valuable information, which is able to help fund managers or investors achieve a higher average investment return or a lower level of volatility under different conditions.     

Population shift bias in tests of space–time interaction

Common to all tests of space–time interaction is the assumption that the population underlying the events of interest exhibits a trajectory of growth that is consistent through time and across space. In practice, however, this assumption is often untenable and, when violated, can introduce population shift bias into the results of these tests. While this problem is widely recognized, more work remains to compare its effect across tests and to determine the extent to which it is a problem for study short periods. This paper quantifies and compares the population shift bias present in the results of the Knox, Mantel, and Jacquez tests of space–time interaction. A simulation study is carried out which quantifies the bias present in each test across a variety of population movement scenarios. Results show a positive relationship between population shift bias and the heterogeneity in population growth across all the tests. They also demonstrate variability in the size of the bias across the three tests for space–time interaction considered. Finally, the results illustrate that population shift bias can be a serious problem for short study periods. Collectively, these findings suggest that an unbiased approach to assessing the significance of space–time interaction test results is needed whenever spatially heterogeneous population change is identified within a study area.     

Two-dimensional diffusion processes as models in lifetime studies

Let X(t) denote the remaining useful lifetime of a machine, and Y(t) be a standard Brownian motion. Assume that the derivative ρ[X(t),?Y(t)] of X(t) is a deterministic function of (at least) Y(t). We consider the two-dimensional degenerate diffusion process (X(t),?Y(t)). We obtain explicit expressions for the expected value of the random variable T(x,?y) denoting the first time the machine must be replaced, or repaired, for various functions ρ[X(t),?Y(t)].     

随机利率与随机波动率环境下的DC型养老金计划

为实现养老金的保值增值,基金管理人将养老金投资于金融市场.假设金融市场包含一种无风险资产、一种股票和一种零息票债券,其中,利率期限结构满足随机仿射利率模型,而股票价格波动率满足Heston随机波动率模型.基金管理人希望寻找一种最优投资组合以最大化其终端财富的期望效用.假设基金管理人对风险的偏好满足幂效用或指数效用,运用随机动态规划原理和变量替换方法,得到幂效用和指数效用下最优投资策略的显式解.最后,通过数值算例分析主要模型参数对最优投资策略的影响.研究结果表明,利率风险、股市波动风险以及缴费率都对缴费确定(DC)型养老金的投资决策产生较大的影响.     

Recovering the initial state of an infinite-dimensional system using observers

Let A be the generator of a strongly continuous semigroup T on the Hilbert space X, and let C be a linear operator from D(A) to another Hilbert space Y (possibly unbounded with respect to X, not necessarily admissible). We consider the problem of estimating the initial state z₀∈D(A) (with respect to the norm of X) from the output function y(t)=CT_tz₀, given for all t in a bounded interval [0,τ]. We introduce the concepts of estimatability and backward estimatability for (A,C) (in a more general way than currently available in the literature), we introduce forward and backward observers, and we provide an iterative algorithm for estimating z₀ from y. This algorithm generalizes various algorithms proposed recently for specific classes of systems and it is an attractive alternative to methods based on inverting the Gramian. Our results lead also to a very general formulation of Russell’s principle, i.e., estimatability and backward estimatability imply exact observability. This general formulation of the principle does not require T to be invertible. We illustrate our estimation algorithms on systems described by wave and Schrödinger equations, and we provide results from numerical simulations.     

A four-stage algorithm for updating a Burrows–Wheeler transform

We present a four-stage algorithm that updates the Burrows–Wheeler Transform of a text T$T$, when this text is modified. The Burrows–Wheeler Transform is used by many text compression applications and some self-index data structures. It operates by reordering the letters of a text T$T$ to obtain a new text bwt(T)$bwt\left(T\right)$ which can be better compressed.     

Faster semi-external suffix sorting

Suffix array (SA) construction is a time-and-memory bottleneck in many string processing applications. In this paper we improve the runtime of a small-space — semi-external — SA construction algorithm by Kärkkäinen (TCS, 2007) [5]. We achieve a speedup in practice of 2–4 times, without increasing memory usage. Our main contribution is a way to implement the “pointer copying” heuristic, used in less space-efficient SA construction algorithms, in a memory-efficient way.     

风险资产收益序列相关的多阶段均值-方差投资组合选择

基于多阶段均值-方差框架, 研究任意多种风险资产存在一般收益序列相关时的投资组合选择问题. 首先, 采用Lagrange 对偶原理与动态规划相结合的方法对模型进行求解, 得到多阶段均值-方差模型的有效投资策略和有效边界的解析表达式; 然后, 证明在含有无风险资产的情形下有效边界仍为均值-标准差平面上的一条射线; 最后, 应用所得结论给出一个具体的实例分析.

     

On the qualitative behaviors of solutions of third order nonlinear differential equations

We present some new results about oscillation and asymptotic behavior of solutions of third order nonlinear differential equations of the form

(r₂(t)(r₁(t)y^′)^′)^′+p(t)y^′+q(t)f(y(g(t)))=0.