Continuous logic in problems of finite automata dynamics

A technique for ordering, classification, and unification of fuzzy (continuous) logic formulas describing dynamical processes in finite automata is proposed. On the example of the class of automata without memory and with simplest input action, it is shown that the technique makes it possible to significantly (in several times) reduce the number of necessary formulas.     

Robust Algorithms for Preemptive Scheduling

Preemptive scheduling problems on parallel machines are classic problems. Given the goal of minimizing the makespan, they are polynomially solvable even for the most general model of unrelated machines. In these problems, a set of jobs is to be assigned to run on a set of m machines. A job can be split into parts arbitrarily and these parts are to be assigned to time slots on the machines without parallelism, that is, for every job, at most one of its parts can be processed at each time. Motivated by sensitivity analysis and online algorithms, we investigate the problem of designing robust algorithms for constructing preemptive schedules. Robust algorithms receive one piece of input at a time. They may change a small portion of the solution as an additional part of the input is revealed. The capacity of change is based on the size of the new piece of input. For scheduling problems, the supremum ratio between the total size of the jobs (or parts of jobs) which may be re-scheduled upon the arrival of a new job j, and the size of j, is called migration factor. We design a strongly optimal algorithm with the migration factor $1-\frac{1}{m}$ for identical machines. Strongly optimal algorithms avoid idle time and create solutions where the (non-increasingly) sorted vector of completion times of the machines is lexicographically minimal. In the case of identical machines this results not only in makespan minimization, but the created solution is also optimal with respect to any ? _p norm (for p>1). We show that an algorithm of a smaller migration factor cannot be optimal with respect to makespan or any other ? _p norm, thus the result is best possible in this sense as well. We further show that neither uniformly related machines nor identical machines with restricted assignment admit an optimal algorithm with a constant migration factor. This lower bound holds both for makespan minimization and for any ? _p norm. Finally, we analyze the case of two machines and show that in this case it is still possible to maintain an optimal schedule with a small migration factor in the cases of two uniformly related machines and two identical machines with restricted assignment.     

The protein structure code: what is its present status?

Current methods of prediction of protein conformation are reviewed and the algorithms on which they rely are presented. For non-homologous proteins and after cross-validation the reported methods exhibit a probability index, i.e. the per cent of correctly predicted residues per predicted residues, of 63-65% with a standard deviation of the order of 7% for three conformational states--helix, beta-strand and coil. This present limitation in the accuracy of predictions that use only the information of the local sequence can be related essentially to the effect of long-range interactions specific for each protein family. The methods based on sequence similarity can improve the accuracy of prediction by expressing explicitly the homology of the protein to be predicted with proteins in the database. In these circumstances the probability index can reach 87% with a standard deviation of 6.6%. This property can be used for modeling homologous proteins by aiding in amino acid sequence alignments. The prediction of the tertiary structure of a protein is still limited to the case of modeling a structure based on the known three-dimensional structure of a homologous protein.     

The dimensional nature of disturbed dreaming: Reply to Weiss (2007).

The authors' proposed model of nightmare formation (see record 2007-06095-006) withstands several criticisms raised in an accompanying commentary article (D. S. Weiss, 2007; see record 2007-06095-007). A principal criticism, that the model lacks convergent and divergent validity, appears to stem from the commenter's application of a strong categorical, as opposed to the authors' use of a dimensional, approach to the model/construct of nightmares. Furthermore, ongoing research continues to support the authors' assumptions about the basic relationship between nightmares and affect distress. Other criticisms of the model, including a failure to account for robust epidemiological differences in nightmares and an ambiguity in the concept of affect distress, are also countered by reference to relevant research findings. A robust gender difference in nightmares (women = men) is particularly compatible with studies demonstrating gender differences in emotion among the physiological and cognitive systems that the authors propose are centrally implicated in nightmare formation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Optimization in terms of interval uncertainty: The determinization method

The current approaches to the optimization of systems under uncertainty are considered. An exact formulation of the problem of the conditional optimization of the target function parameters and limitations under interval uncertainty is given. A determinization method allowed us to solve the problem by reducing it to two completely determined ones of conditional optimization of the same type is stated and proved.     

Approximation Algorithms for Quickest Spanning Tree Problems

Let $G=(V,E)$ be an undirected multigraph with a special vertex ${\it root} \in V$, and where each edge $e \in E$ is endowed with a length $l(e) \geq 0$ and a capacity $c(e) > 0$. For a path $P$ that connects $u$ and $v$, the {\it transmission time} of $P$ is defined as $t(P)=\mbox{\large$\Sigma$}_{e \in P} l(e) + \max_{e \in P}\!{(1 / c(e))}$. For a spanning tree $T$, let $P_{u,v}^T$ be the unique $u$--$v$ path in $T$. The {\sc quickest radius spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max _{v \in V} t(P^T_{root,v})$ is minimized. In this paper we present a 2-approximation algorithm for this problem, and show that unless $P =NP$, there is no approximation algorithm with a performance guarantee of $2 - \epsilon$ for any $\epsilon >0$. The {\sc quickest diameter spanning tree problem} is to find a spanning tree $T$ of $G$ such that $\max_{u,v \in V} t(P^T_{u,v})$ is minimized. We present a ${3 \over 2}$-approximation to this problem, and prove that unless $P=NP$ there is no approximation algorithm with a performance guarantee of ${3 \over 2}-\epsilon$ for any $\epsilon >0$.     

User assisted separation of reflections from a single image using a sparsity prior

When we take a picture through transparent glass the image we obtain is often a linear superposition of two images: the image of the scene beyond the glass plus the image of the scene reflected by the glass. Decomposing the single input image into two images is a massively ill-posed problem: in the absence of additional knowledge about the scene being viewed there are an infinite number of valid decompositions. In this paper we focus on an easier problem: user assisted separation in which the user interactively labels a small number of gradients as belonging to one of the layers. Even given labels on part of the gradients, the problem is still ill-posed and additional prior knowledge is needed. Following recent results on the statistics of natural images we use a sparsity prior over derivative filters. This sparsity prior is optimized using the terative reweighted least squares (IRLS) approach. Our results show that using a prior derived from the statistics of natural images gives a far superior performance compared to a Gaussian prior and it enables good separations from a modest number of labeled gradients.