Metrical properties of the set of bent functions in view of duality

In the paper, we give a review of metrical properties of the entire set of bent functions and its significant subclasses of self-dual and anti-self-dual bent functions. We present results for iterative construction of bent functions in n + 2 variables based on the concatenation of four bent functions and consider related open problem proposed by one of the authors. Criterion of self-duality of such functions is discussed. It is explored that the pair of sets of bent functions and affine functions as well as a pair of sets of self-dual and anti-self-dual bent functions in n > 4 variables is a pair of mutually maximally distant sets that implies metrical duality. Groups of automorphisms of the sets of bent functions and (anti-)self-dual bent functions are discussed. The solution to the problem of preserving bentness and the Hamming distance between bent function and its dual within automorphisms of the set of all Boolean functions in n variables is considered

О некоторых свойствах самодуальных обобщенных бент-функций

Бент-функции вида FI) ^ , где q ^ 2 — натуральное число, называются обобщёнными бент-функциями. Обобщённые бент-функции, для которых можно определить дуальную бент-функцию, называются регулярными. Регулярная обобщённая бент-функция называется самодуальной, если она совпадает со своей дуальной. Получены необходимые и достаточные условия самодуальности обобщённых бент-функций из класса Елисеева — Мэйорана — МакФарланда. Представлен полный спектр расстояний Ли между данными функциями. Доказано несуществование аффинных самодуальных обобщённых бент-функций. Приведён класс изомет- ричных отображений, сохраняющих самодуальность обобщённой бент-функции. С помощью данных отображений получена уточнённая классификация самодуальных бент-функций вида F| ^ Z4. Bent functions of the form Fn ^ , where q ^ 2 is a positive integer, are known as generalized bent (gbent) functions. A gbent function for which it is possible to define a dual gbent function is called regular. A regular gbent function is said to be self-dual if it coincides with its dual. We obtain the necessary and sufficient conditions for the self-duality of gbent functions from Eliseev — Maiorana — McFarland class. We find the complete Lee distance spectrum between all self-dual functions in this class and obtain that the minimal Lee distance between them is equal to q ■ 2n-3. For Boolean case, there are no affine bent functions and self-dual bent functions, while it is known that for generalized case affine bent functions exist, in particular, when q is divisible by 4. We prove the non-existence of affine self-dual gbent functions for any natural even q. A new class of isometries preserving self-duality of a gbent function is presented. Based on this, a refined classification of self-dual gbent functions of the form F2 ^ is given

Identification of direct residue contacts in protein-protein interaction by message passing

Understanding the molecular determinants of specificity in protein-protein interaction is an outstanding challenge of postgenome biology. The availability of large protein databases generated from sequences of hundreds of bacterial genomes enables various statistical approaches to this problem. In this context covariance-based methods have been used to identify correlation between amino acid positions in interacting proteins. However, these methods have an important shortcoming, in that they cannot distinguish between directly and indirectly correlated residues. We developed a method that combines covariance analysis with global inference analysis, adopted from use in statistical physics. Applied to a set of >2,500 representatives of the bacterial two-component signal transduction system, the combination of covariance with global inference successfully and robustly identified residue pairs that are proximal in space without resorting to ad hoc tuning parameters, both for heterointeractions between sensor kinase (SK) and response regulator (RR) proteins and for homointeractions between RR proteins. The spectacular success of this approach illustrates the effectiveness of the global inference approach in identifying direct interaction based on sequence information alone. We expect this method to be applicable soon to interaction surfaces between proteins present in only 1 copy per genome as the number of sequenced genomes continues to expand. Use of this method could significantly increase the potential targets for therapeutic intervention, shed light on the mechanism of protein-protein interaction, and establish the foundation for the accurate prediction of interacting protein partners.Comment: Supplementary information available on http://www.pnas.org/content/106/1/67.abstrac

О метрических свойствах множества самодуальных бент-функций

Приводится обзор известных метрических свойств множества самодуальных бент- функций. Бент-функция называется самодуальной, если она совпадает со своей дуальной бент-функцией, и анти-самодуальной, если совпадает с отрицанием своей дуальной. Приводится полный спектр расстояний Хэмминга между самодуальными бент-функциями из класса Мэйорана — МакФарланда. Даются результаты, касающиеся характеризации булевых функций, находящихся на максимально возможном удалении от множества самодуальных бент-функций. Описаны группы автоморфизмов множеств самодуальных и анти-самодуальных бент-функций от n переменных, автоморфизмы множества булевых функций от n переменных, которые меняют местами множества самодуальных и анти-самодуальных бент- функций, изометричные отображения, сохраняющие неизменным отношение Рэлея каждой булевой функции от n переменных. Даётся характеризация всех изо- метричных отображений, сохраняющих максимальную нелинейность и расстояние Хэмминга между каждой бент-функций и дуальной к ней

Cyclotomic trace codes

A generalization of Ding’s construction is proposed that employs as a defining set the collection of the sth powers (s ≥ 2) of all nonzero elements in GF(pm), where p ≥ 2 is prime. Some of the resulting codes are optimal or near-optimal and include projective codes over GF(4) that give rise to optimal or near optimal quantum codes. In addition, the codes yield interesting combinatorial structures, such as strongly regular graphs and block designs

The group of automorphisms of the set of self-dual bent functions

A bent function is a Boolean function in even number of variables which is on the maximal Hamming distance from the set of affine Boolean functions. It is called self-dual if it coincides with its dual. It is called anti-self-dual if it is equal to the negation of its dual. A mapping of the set of all Boolean functions in n variables to itself is said to be isometric if it preserves the Hamming distance. In this paper we study isometric mappings which preserve self-duality and anti-self-duality of a Boolean bent function. The complete characterization of these mappings is obtained for n>2. Based on this result, the set of isometric mappings which preserve the Rayleigh quotient of the Sylvester Hadamard matrix, is characterized. The Rayleigh quotient measures the Hamming distnace between bent function and its dual, so as a corollary, all isometric mappings which preserve bentness and the Hamming distance between bent function and its dual are described

The Structure and Activation of Soluble Guanylate Cyclase

The biochemical signaling pathways that involve gaseous primary signaling molecules have only been characterized in the last three decades, due to the small diversity of diatomic gases and the lack of other known physiological functions of these gases (apart from O2 as the terminal electron acceptor in oxidative phosphorylation). In general, certain events must take place for any process to be considered biochemical signaling: the primary signaling molecule must be synthesized and excreted from the generator cell or be present or absent in the environment, that signaling molecule must come in contact with its specific receptor molecule within the receiving cell, and the receptor molecule must transduce the primary singling molecule into a secondary signal which activates downstream signaling pathways. Only a pathway that is comprised of signal generation, the primary signal, and signal reception constitutes a complete biochemical signaling pathway. In spite of the relatively recent discovery, gaseous signaling molecules control critical signaling pathways in many aspects of organismal physiology.In the 1980s, two different lines of research serendipitously came together to describe the first gaseous biochemical signaling pathway. The first was pharmacologists’ observation that vasculature that had the endothelium removed would constrict, and thus there must be an Endothelium Derived Relaxation Factor (EDRF) that maintained appropriate vasculature tone. Curiously, EDRF had the exact same chemical properties as nitric oxide (NO), however there was no known biotic source of this toxic gas. The second line of research centered on the observation that excreted nitrates spiked in concentration when sickness was incurred, even when nitrate intake remained the same. This led to the discovery that macrophages synthesize the cytotoxic agent NO to attack invading pathogens, and thus a biotic source of NO had been discovered. The EDRF and NO were shown to be one and the same, and this coupled with the fact that soluble guanylate cyclase had been known to be stimulated by NO since the 1970s provided the receptor of the first gaseous biochemical signaling pathway.The enzyme responsible for the generation of NO is nitric oxide synthase (NOS) (EC 1.14.13.39). NOS catalyzes the 5-electron oxidation of arginine to citrulline and NO. There are three different isoforms of NOS in Homo sapiens, inducible NOS (iNOS), endothelial NOS (eNOS), and neuronal (nNOS). Nitric oxide synthases are activated by calcium-bound calmodulin (Ca2+-CaM). iNOS has a high affinity for Ca2+-CaM, and thus is regulated at the transcriptional level in macrophages where it synthesizes NO at sites of infection or inflammation. eNOS and nNOS have lower affinity for Ca2+-CaM and are constitutively expressed, which allows calcium gradients in neurons and endothelial cells to control the activation of these isoforms. For example, when endothelial cells hyperpolarize due to high blood pressure, intracellular concentrations of Ca2+ increase up to ten-fold which in turn increases Ca2+-CaM concentration and thus activates eNOS.Activated eNOS generates NO at nanomolar concentrations, which diffuses to nearby smooth muscle cells that express the mammalian NO receptor, soluble guanylate cyclase (sGC) (EC 4.6.1.2). sGC is a heterodimeric hemeoprotein which can sense NO at nanomolar concentrations. When NO binds to sGC, the enzyme increases its catalytic activity of cyclizing 5′-guanosine triphosphate (GTP) to 3′,5′-cyclic guanosine monophosphate (cGMP). The molecular mechanisms by which NO activates sGC are not completely understood. In particular, it is clear from experiments both in vitro and in cells that one equivalent of NO does not activate sGC to its maximal activity but only to a low activity state. Excess NO must be present in order to completely stimulate the enzyme. If that excess NO is removed either with a buffer exchange or a chemical trap, the enzyme returns to a low activity state. The increase in cellular concentration of cGMP activates a variety of downstream signaling proteins, including cGMP-dependent protein kinases, cGMP-regulated ion channels, and phosphodiesterases that mediate the downstream cell signaling cascade. The resultant phenotype of these cellular signaling molecules is the relaxation of the smooth muscle cells, the dilation of the vasculature, and the decrease of overall blood pressure. Thus, any malfunctions of this pathway can result in too high of blood pressure and increased risk of cardiovascular diseases.The NOS-NO-sGC-cGMP signaling pathway has been the target for stimulating therapeutics to treat forms of high blood pressure. A screen of small molecules that induce platelet aggregation found that the chemically synthesized benzylindazole YC-1 was able to stimulate sGC in a heme-dependent manner. Significant efforts in medicinal chemistry in the following two decades yielded riociguat, the first FDA-approved sGC stimulator that is used to treat certain forms of pulmonary hypertension. However, the specific binding site of YC-1 derived compounds on sGC and the reason for the specificity of these types of molecules against the soluble form of guanylate cyclases has not been elucidated. Additionally, atypical soluble guanylate cyclases have been described that sense O2 instead of NO. Thus, the possibility exists for gases other than NO and O2 to function as signaling molecules in eukaryotic organisms. These outstanding questions will be answered in the following thesis entitled: The Structure and Activation of Soluble Guanylate Cyclase

Nested Dynamics of Metropolitan Processes and Policies - MELBOURNE

BACKGROUND PAPERS FOR THE METROPOLITAN STUDY: 1 -- The Project "Nested Dynamics of Metropolitan Processes and Policies" was initiated by the Regional and Urban Development Group in 1983 and work on this collaborative study started in 1983. This series of contributions represent "entry tickets" to the Project, i.e., initial statements by authors from individual metropolitan regions that are participating in the Project's network. The aim of these papers is threefold. First, to provide some background information describing the processes of change within four principal subsystems: population, housing, economy, and transportation. Second, to identify major trends and crucial policy issues which are to constitute a focus for the subsequent analytical and modeling work. Third, to facilitate comparative studies of development paths among these regions and the dynamic interdependencies between the above subsystems. The background material contained in this paper pertains to the Melbourne metropolitan region