Improved algorithms for online load balancing

We consider an online load balancing problem and its extensions in the framework of repeated games. On each round, the player chooses a distribution (task allocation) over $K$ servers, and then the environment reveals the load of each server, which determines the computation time of each server for processing the task assigned. After all rounds, the cost of the player is measured by some norm of the cumulative computation-time vector. The cost is the makespan if the norm is $L_\infty$-norm. The goal is to minimize the regret, i.e., minimizing the player's cost relative to the cost of the best fixed distribution in hindsight. We propose algorithms for general norms and prove their regret bounds. In particular, for $L_\infty$-norm, our regret bound matches the best known bound and the proposed algorithm runs in polynomial time per trial involving linear programming and second order programming, whereas no polynomial time algorithm was previously known to achieve the bound.Comment: 16 pages; typos correcte

Locally Optimal Load Balancing

This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of adjacent nodes differ by at most $1$. If the graph is a path ($\Delta = 2$), it is easy to solve the fractional version of the problem in $O(L)$ communication rounds, independently of the number of nodes. We show that this is tight, and we show that it is possible to solve also the discrete version of the problem in $O(L)$ rounds in paths. For the general case ($\Delta > 2$), we show that fractional load balancing can be solved in $\operatorname{poly}(L,\Delta)$ rounds and discrete load balancing in $f(L,\Delta)$ rounds for some function $f$, independently of the number of nodes.Comment: 19 pages, 11 figure

Generalizing movements with information-theoretic stochastic optimal control

Stochastic optimal control is typically used to plan a movement for a specific situation. Although most stochastic optimal control methods fail to generalize this movement plan to a new situation without replanning, a stochastic optimal control method is presented that allows reuse of the obtained policy in a new situation, as the policy is more robust to slight deviations from the initial movement plan. To improve the robustness of the policy, we employ information-theoretic policy updates that explicitly operate on trajectory distributions instead of single trajectories. To ensure a stable and smooth policy update, the ”distance” is limited between the trajectory distributions of the old and the new control policies. The introduced bound offers a closed-form solution for the resulting policy and extends results from recent developments in stochastic optimal control. In contrast to many standard stochastic optimal control algorithms, the current approach can directly infer the system dynamics from data points, and hence can also be used for model-based reinforcement learning. This paper represents an extension of the paper by Lioutikov et al. (“Sample-Based Information-Theoretic Stochastic Optimal Control,” Proceedings of 2014 IEEE International Conference on Robotics and Automation (ICRA), IEEE, Piscataway, NJ, 2014, pp. 3896–3902). In addition to revisiting the content, an extensive theoretical comparison is presented of the approach with related work, additional aspects of the implementation are discussed, and further evaluations are introduced

Statistical mechanics of budget-constrained auctions

Finding the optimal assignment in budget-constrained auctions is a combinatorial optimization problem with many important applications, a notable example being the sale of advertisement space by search engines (in this context the problem is often referred to as the off-line AdWords problem). Based on the cavity method of statistical mechanics, we introduce a message passing algorithm that is capable of solving efficiently random instances of the problem extracted from a natural distribution, and we derive from its properties the phase diagram of the problem. As the control parameter (average value of the budgets) is varied, we find two phase transitions delimiting a region in which long-range correlations arise.Comment: Minor revisio

Prophet Inequalities for IID Random Variables from an Unknown Distribution

A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: given a sequence of random variables X1, . . . , Xn drawn independently from a distribution F , the goal is to choose a stopping time τ so as to maximize α such that for all distributions F we have E[Xτ ] ≥ α · E[maxt Xt ]. What makes this problem challenging is that the decision whether τ = t may only depend on the values of the random variables X1, . . . , Xt and on the distribution F . For a long time the best known bound for the problem had been α ≥ 1 − 1/e ≈ 0.632, but quite recently a tight bound of α ≈ 0.745 was obtained. The case where F is unknown, such that the decision whether τ = t may depend only on the values of the random variables X1, . . . , Xt , is equally well motivated but has received much less attention. A straightforward guarantee for this case of α ≥ 1/e ≈ 0.368 can be derived from the solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F , and show that even with o(n) samples α ≤ 1/e. On the other hand, n samples allow for a significant improvement, while O(n2) samples are equivalent to knowledge of the distribution: specifically, with n samples α ≥ 1 − 1/e ≈ 0.632 and α ≤ ln(2) ≈ 0.693, and with O(n2) samples α ≥ 0.745 − ε for any ε > 0

Understanding the role of shame and its consequences in female hypersexual behaviours: A pilot study

Background and aims: Hypersexuality and sexual addiction among females is a little understudied phenomenon. Shame is thought to be intrinsic to hypersexual behaviours, especially in women. Therefore, the aim of this study was to understand both hypersexual behaviours and consequences of hypersexual behaviours and their respective contributions to shame in a British sample of females (n = 102). Methods: Data were collected online via Survey Monkey. Results: Results showed the Sexual Behaviour History (SBH) and the Hypersexual Disorder Questionnaire (HDQ) had significant positive correlation with scores on the Shame Inventory. The results indicated that hypersexual behaviours (HBI and HDQ) were able to predict a small percentage of the variability in shame once sexual orientation (heterosexual vs. non-heterosexual) and religious beliefs (belief vs. no belief) were controlled for. Results also showed there was no evidence that religious affiliation and/or religious beliefs had an influence on the levels of hypersexuality and consequences of sexual behaviours as predictors of shame. Conclusions: While women in the UK are rapidly shifting to a feminist way of thinking with or without technology, hypersexual disorder may often be misdiagnosed and misunderstood because of the lack of understanding and how it is conceptualised. The implications of these findings are discussed

Wear Minimization for Cuckoo Hashing: How Not to Throw a Lot of Eggs into One Basket

We study wear-leveling techniques for cuckoo hashing, showing that it is possible to achieve a memory wear bound of $\log\log n+O(1)$ after the insertion of $n$ items into a table of size $Cn$ for a suitable constant $C$ using cuckoo hashing. Moreover, we study our cuckoo hashing method empirically, showing that it significantly improves on the memory wear performance for classic cuckoo hashing and linear probing in practice.Comment: 13 pages, 1 table, 7 figures; to appear at the 13th Symposium on Experimental Algorithms (SEA 2014

Dehydroepiandrosterone stimulates nerve growth factor and brain derived neurotrophic factor in cortical neurons

Due to the increasing cases of neurodegenerative diseases in recent years, the eventual goal of nerve repair is very important. One approach for achieving a neuronal cell induction is by regenerative pharmacology. Nerve growth factor (NGF) and brain derived neurotrophic factor (BDNF) are neurotrophins that play roles in neuronal development, differentiation, and protection. On the other hand, dehydroepiandrosterone (DHEA) is a neurosteroid which has multiple actions in the nervous system. DHEA could be an important agent in regenerative pharmacology for neuronal differentiation during tissue regeneration. In this study, we investigated the possible role of DHEA to modulate NGF and BDNF production. The in vivo level of neurotrophins expression was demonstrated by ELISA in rat harvested brain cortex. Also neurotrophins expression after DHEA treatment was revealed by the increased neurite extension, immunostaining, and BrdU labeling in rats. Anti-NGF and anti-BDNF antibodies were used as suppressive agents on neurogenesis. The results showed that NGF and BDNF are overproduced after DHEA treatment but there is not any overexpression for NT-3 and NT-4. Also DHEA increased neurite extension and neural cell proliferation significantly. Overall, DHEA might induce NGF and BDNF neurotrophins overproduction in cortical neurons which promotes neural cell protection, survival, and proliferation. © 2013 Anahita Rahmani et al