Linear complexity over F_q and over F_{q^m} for linear recurring sequences

Since the \F_q-linear spaces \F_q^m and \F_{q^m} are isomorphic, an $m$-fold multisequence $\mathbf{S}$ over the finite field \F_q with a given characteristic polynomial f \in \F_q[x], can be identified with a single sequence $\mathcal{S}$ over \F_{q^m} with characteristic polynomial $f$. The linear complexity of $\mathcal{S}$, which we call the generalized joint linear complexity of $\mathbf{S}$, can be significantly smaller than the conventional joint linear complexity of $\mathbf{S}$. We determine the expected value and the variance of the generalized joint linear complexity of a random $m$-fold multisequence $\mathbf{S}$ with given minimal polynomial. The result on the expected value generalizes a previous result on periodic $m$-fold multisequences. Finally we determine the expected drop of linear complexity of a random $m$-fold multisequence with given characteristic polynomial $f$, when one switches from conventional joint linear complexity to generalized joint linear complexity

Generalized joint linear complexity of linear recurring multisequences

The joint linear complexity of multisequences is an important security measure for vectorized stream cipher systems. Extensive research has been carried out on the joint linear complexity of $N$-periodic multisequences using tools from Discrete Fourier transform. Each $N$-periodic multisequence can be identified with a single $N$-periodic sequence over an appropriate extension field. It has been demonstrated that the linear complexity of this sequence, the so called generalized joint linear complexity of the multisequence, may be considerably smaller than the joint linear complexity, which is not desirable for vectorized stream ciphers. Recently new methods have been developed and results of greater generality on the joint linear complexity of multisequences consisting of linear recurring sequences have been obtained. In this paper, using these new methods, we investigate the relations between the generalized joint linear complexity and the joint linear complexity of multisequences consisting of linear recurring sequences

Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes

Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring. The structure of the ambient ring of polycyclic codes over GR(p^a,m) and generating sets for its ideals are considered. Along with some structure details of the ambient ring, the existance of a certain type of generating set for an ideal is proven.Comment: arXiv admin note: text overlap with arXiv:0906.400

Information flow and optimization in transcriptional control

In the simplest view of transcriptional regulation, the expression of a gene is turned on or off by changes in the concentration of a transcription factor (TF). We use recent data on noise levels in gene expression to show that it should be possible to transmit much more than just one regulatory bit. Realizing this optimal information capacity would require that the dynamic range of TF concentrations used by the cell, the input/output relation of the regulatory module, and the noise levels of binding and transcription satisfy certain matching relations. This parameter-free prediction is in good agreement with recent experiments on the Bicoid/Hunchback system in the early Drosophila embryo, and this system achieves ~90% of its theoretical maximum information transmission.Comment: 5 pages, 4 figure

A stochastic spectral analysis of transcriptional regulatory cascades

The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here we introduce the spectral method for computation of the joint probability distribution over all species in a biological network. The spectral method exploits the natural eigenfunctions of the master equation of birth-death processes to solve for the joint distribution of modules within the network, which then inform each other and facilitate calculation of the entire joint distribution. We illustrate the method on a ubiquitous case in nature: linear regulatory cascades. The efficiency of the method makes possible numerical optimization of the input and regulatory parameters, revealing design properties of, e.g., the most informative cascades. We find, for threshold regulation, that a cascade of strong regulations converts a unimodal input to a bimodal output, that multimodal inputs are no more informative than bimodal inputs, and that a chain of up-regulations outperforms a chain of down-regulations. We anticipate that this numerical approach may be useful for modeling noise in a variety of small network topologies in biology

Benefits of omalizumab on anxiety and depression in patients with severe asthma

Background: Asthma is one of the most common chronic diseases and may cause psychiatric disorders affecting the patients’ quality of life. In our study, we evaluated the effect of omalizumab treatment on anxiety disorder and depression using Beck Depression Scale (BDS) and State Trait Anxiety Inventory (STAI). Methods: Anxiety level was determined with STAI, whereas depression level was evaluated by BDS. Patients were asked to mark the questionnaires to reflect their emotional state before treatment, and to reflect their emotions they are feeding in the current moment. All patients receiving omalizumab treatment were included in the study. Patients with known neuropsychiatric disorder were excluded from the study. Results: A total of 20 patients with mean age of 50.25 years were enrolled in the study. Gender distribution was: 5(25%) male patients and 15(75%) female patients. All patients with severe asthma received omalizumab treatment. The omalizumab treatment period was shown for mean 17.6 months (2-40 months). In anxiety scales, there was statistically significant difference compared with pretreatment and posttreatment periods. Depression (moderate to severe) was present in 12 patients before omalizumab treatment and 3 patients after omalizumab treatment. Conclusions: Uncontrolled asthma as a chronic disorder can cause depressive symptoms and worsen quality of life. We believe by controlling asthma, quality of life will improvein such patients. In appropriate indication, omalizumab can improve depression and anxiety in asthma patients

Fibre products of superelliptic curves and codes therefrom

A method of constructing long geometric Goppa codes coming from fiber products of superelliptic curves is presented. A family of smooth projective curves with a lot of Fq-rational points are needed to produce a family of asymptotically good geometric Goppa codes. The genus in every such family is considerably less than the number of rational points, so the corresponding geometric Goppa codes have rather good parameters. Examples of such families are provided by modular curves, by Drinfeld modular curves, and by Artin-Schreier coverings of the projective line

Noise and multistability in gene regulatory networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2004.Includes bibliographical references (leaves 103-112).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Proteins are the functional machinery in living cells. Proteins interact with each other and bind to DNA to form so-called gene regulatory networks and in this way regulate the level, location and timing of expression of other proteins. Cells implement feedback loops to create a memory of their gene expression states. In this way, every differentiated cell in a multicellular organism remembers its expression profile throughout its life. On the other hand, biochemical reactions that take place during gene expression involve small numbers of molecules, and are therefore dominated by large concentration fluctuations. This intrinsic noise has the potential to corrupt memory storage and might result in random transitions between different gene expression states. In the first part of my thesis, I will discuss how the fluctuations in gene expression levels are regulated. The results provided the first experimental evidence that cells can regulate noise in their gene expression by tuning their genetic parameters. In the second half of my thesis, I will discuss how cells create memory by experimentally studying a gene regulatory network that implements a positive feedback loop. A positive feedback loop with nonlinear interactions creates two distinct stable gene expression states. A phase diagram, coupled with a mathematical model of the network, was used to quantitatively investigate the biochemical processes in this network. The response of the network depends on its previous history (hysteresis). Despite the fluctuations in the gene expression, the memory of the gene expression state is preserved for a long time for a broad range of system parameters.(cont.) On the other hand, for some of the parameters, noise causes random transitions of the cells between different gene expression states and results in a bimodal response. Finally, the hysteretic response of the natural system is experimentally converted to an ultrasensitive graded response as predicted by our model.by Ertugrul M. Ozbudak.Ph.D