An Operational Characterization for Optimal Observation of Potential Properties in Quantum Theory and Signal Analysis

Quantum logic introduced a paradigm shift in the axiomatization of quantum theory by looking directly at the structural relations between the closed subspaces of the Hilbert space of a system. The one dimensional closed subspaces correspond to testable properties of the system, forging an operational link between theory and experiment. Thus a property is called actual, if the corresponding test yields “yes” with certainty. We argue a truly operational definition should include a quantitative criterion that tells us when we ought to be satisfied that the test yields “yes” with certainty. This question becomes particularly pressing when we inquire how the usual definition can be extended to cover potential, rather than actual properties. We present a statistically operational candidate for such an extension and show that its representation automatically captures some essential Hilbert space structure. If it is the nature of observation that is responsible for the Hilbert space structure, then we should be able to give examples of theories with scope outside the domain of quantum theory, that employ its basic structure, and that describe the optimal extraction of information. We argue signal analysis is such an example. This work was supported by the Flemish Fund for Scientific Research (FWO) project G.0362.03N.     

Planck’s Constant in the Light of Quantum Logic

The goal of quantum logic is the “bottom-top” reconstruction of quantum mechanics. Starting from a weak quantum ontology, a long sequence of arguments leads to quantum logic, to an orthomodular lattice, and to the classical Hilbert spaces. However, this abstract theory does not yet contain Planck’s constant ℏ. We argue, that ℏ can be obtained, if the empty theory is applied to real entities and extended by concepts that are usually considered as classical notions. Introducing the concepts of localizability and homogeneity we define objects by symmetry groups and systems of imprimitivity. For elementary systems, the irreducible representations of the Galileo group are projective and determined only up to a parameter z, which is given by z=m/ℏ, where m is the mass of the particle and ℏ Planck’s constant. We show that ℏ has a meaning within quantum mechanics, irrespective of use the of classical concepts in our derivation.     

The mixed volume optimization problem

The mixed volume optimization problem is to determine the point of duality Q for a given convex set K that minimizes the “mixed volume” of the associated polar set (K^*;Q). In the plane, the mixed volumes translate as the area and length; in space, the mixed volumes include the volume, surface area, and mean width. In this paper, the geometric optimization problems associated with minimizing mixed volumes are examined from two perspectives: enumerative search and symbolic computation. The problem of minimizing the polar area through an enumerative search is first considered. The dual polygon (P_m^*;Q) is constructed for an arbitrary point of duality QP_m° by using an algebraic correspondence between the edges of P_m and the vertices of (P_m^*;Q), and the area of (P_m^*;Q), A(P^*_m;Q), is calculated and minimized using naive search techniques. A result due to Santaló is applied to verify the minimizing solution, and computational tests are described for various classes of randomly generated polygons. Statistical evidence indicates that a “good” approximation to the minimum area polar polygon occurs when the duality point is located at the center-of-gravity of P_m. The polar area problem is then investigated using symbolic procedures. Explicit symbolic expressions for the polar area and length functionals are computed and solved directly using the differential optimality conditions and Newton's iterative method of solution. The mixed volume and surface area functionals are formulated and solved using numerical products, and the mean width functional is described. Examples are used throughout to illustratethe methodology.     

A statistical method for predicting alpha-helical and beta-sheet regions in proteins from their amino acidic sequences

Summary In this paper we propose a new method to predict the secondary structure of proteins from sequence data. A satisfactory improvement of the available efficiency of prediction is obtained. The described method takes into account the frequency of each pair of amino acids in alpha-helical, beta-sheet and random coil regions according to previous results that the sequences of amino acidic residues in these regions are autocorrelated. The rules of the method are not derived from the analysis of the regions of proteins with a known secondary structure, but they are instead based on statistical considerations. In such a way the obtained value of efficiency of the method (88%) has a high reliability: in fact, it is correct to test a method only on the data not used to construct it. A new definition of efficiency of a predictive method is given to resolve the ambiguities arising from the previously accepted definitions.

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Riassunto In questo lavoro si propone un nuovo algoritmo per predire la struttura secondaria di una proteina dall’analisi della sua sequenza aminoacidica, con il quale si è ottenuto un significativo miglioramento delle efficienze di previsione della struttura secondaria disponibili fino ad ora. Il metodo descritto tiene conto della frequenza delle coppie adiacenti di aminoacidi nelle regioni ad alpha-helix, beta sheet e random coil, in accordo con il nostro precedente risultato che in tali regioni le sequenze aminoacidiche sono autocorrelate. Le regole usate non derivano dall’analisi delle regioni di proteine con una struttura secondaria nota, ma sono invece basate esclusivamente su considerazioni statistiche. In tal modo il valore ottenuto per l’efficienza del metodo (88%) ha un’alta affidabilità, essendo corretto controllare un metodo solo sui dati non utilizzati per la sua costruzione. Per risolvere le ambiguità esistenti, inoltre, si dà qui una nuova definizione di efficienza per un metodo di previsione di strutture secondarie.

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Резюме В этой работе предлагается новый метод для предсказания вторичной структуры белков, исходя из последовательности аминокислот. Получается существенное улучшение эффективности предсказания. Предложенный метод учитывает частоту каждой пары аминокислот в альфа-спиральной области, бета-слоистой области и в области случайных спиралей, в соответствии с предыдущими результатами, согласно которым последовательности аминокислот в этих областях являются автокоррелированными. Правила метода не выводятся из анализа областей белков с известной вторичной структурой, а основываются на статистических рассмотрениях. Полученное значение эффективности (88%) имеет высокую надежность. Корректность метода проверялась не только на данных, использованных для его конструирования. Предлагается новое определение эффективности для разрешения неоднозначностей, связанных с ранее принятыми определениями.

     

条形爆炸逻辑器件之功能研究

通过敞式观察条纹技术(OVST)和火花隙或者多条纹技术(MST)相配合,可以较为简单地让条形起爆逻辑器件(这里是指一种8管条形同步引信)理想引爆,随之使传爆药栓点火并妥善传爆到总管烈性炸药。     

Exhibiting Wide Families of Maximal Intermediate Propositional Logics with the Disjunction Property

We provide results allowing to state, by the simple inspection of suitable classes of posets (propositional Kripke frames), that the corresponding intermediate propositional logics are maximal among the ones which satisfy the disjunction property. Starting from these results, we directly exhibit, without using the axiom of choice, the Kripke frames semantics of 2^No maximal intermediate propositional logics with the disjunction property. This improves previous evaluations, giving rise to the same conclusion but made with an essential use of the axiom of choice, of the cardinality of the set of the maximal intermediate propositional logics with the disjunction property. Mathematics Subject Classification: 03B55, 03C90.     

可编程光学并行模糊逻辑门

提出了可级联的光学并行模糊逻辑门系统，十六种模糊逻辑运算可通过编程偏振半波片的状态而得到实现，语言中给出了实验结果。     

基于接地开关理论的电流型多值CMOS电路设计

以开关信号理论为指导，对电流型CMOS电路中开关变量和信号变量的相互作用进行了分析，并引入了适用于CMOS电路的电源开关理论。基于接地电流开关理论，对几类重要的三值CMOS电路进行了设计。结果表明，应用该理论能获得简单的电路设计。从而进一步完善了开关级逻辑电路设计的研究。     

Absolute Continuity and the Uniqueness of the Constructive Functional Calculus

The constructive functional calculus for a sequence of commuting selfadjoint operators on a separable Hilbert space is shown to be independent of the orthonormal basis used in its construction. The proof requires a constructive criterion for the absolute continuity of two positive measures in terms of test functions. Mathematics Subject Classification: 03F60, 46S30, 47S30.     

Hypothesis on the function of non-coding DNA and hnRNA

Summary Half-way through what North American scientists have nominated the ?Decade of the Brain?, the author brings to lights a completely new approach to the problem of the function of non-coding DNA and heterogeneous nuclear RNA whose role, for the moment, remains unknown. This allows the author to put forward an innovative hypothesis on intelligence and memory within the framework of a more logical and coherent unitarian vision of the structure and evolution of living things. The conjecture put forward in this paper, while plausible, has no experimental support. The Referees have expressed perplexity on this regard. Anyway, the Direction ofIl Nuovo Cimento considers it worthwhile to expose the readers to the challenge of this conjecture, hoping that it may trigger a lively debate. The author of this paper has agreed to not receive the proofs for correction.