Systems with Single Degree of Freedom and the Interpretation of Quantum Mechanics

Physical systems can store information and their informational properties are governed by the laws of information. In particular, the amount of information that a physical system can convey is limited by the number of its degrees of freedom and their distinguishable states. Here we explore the properties of the physical systems with absolutely one degree of freedom. The central point in these systems is the tight limitation on their information capacity. Discussing the implications of this limitation we demonstrate that such systems exhibit a number of features, such as randomness, no-cloning, and non-commutativity, which are peculiarities attributed to quantum mechanics (QM). After demonstrating many astonishing parallels to quantum behavior, we postulate an interpretation of quantum physics as the physics of systems with a single degree of freedom. We then show how a number of other quantum conundrum can be understood by considering the informational properties of the systems and also resolve the EPR paradox. In the present work, we assume that the formalism of the QM is correct and well-supported by experimental verification and concentrate on the interpretational aspects of the theory

Subspace Leakage Analysis and Improved DOA Estimation with Small Sample Size

Classical methods of DOA estimation such as the MUSIC algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix. For a small number of samples, such methods are exposed to performance breakdown, as the sample covariance matrix can largely deviate from the true covariance matrix. In this paper, the problem of DOA estimation performance breakdown is investigated. We consider the structure of the sample covariance matrix and the dynamics of the root-MUSIC algorithm. The performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace. In this paper, the subspace leakage is theoretically derived. We also propose a two-step method which improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced. Furthermore, we introduce a phenomenon named as root-swap which occurs in the root-MUSIC algorithm in the low sample size region and degrades the performance of the DOA estimation. A new method is then proposed to alleviate this problem. Numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods. Moreover, the proposed algorithms are combined with the pseudo-noise resampling method to further improve the performance.Comment: 37 pages, 10 figures, Submitted to the IEEE Transactions on Signal Processing in July 201

Cramer-Rao Bound for Sparse Signals Fitting the Low-Rank Model with Small Number of Parameters

In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse representation in a finite basis, they possess a sparse structure which makes it possible to recover the signal from compressed measurements. We study the statistical performance bound for parameter estimation in the low-rank signal model from compressed measurements. Specifically, we derive the Cramer-Rao bound (CRB) for a generic low-rank model and we show that the number of compressed samples needs to be larger than the number of sources for the existence of an unbiased estimator with finite estimation variance. We further consider the applications to direction-of-arrival (DOA) and spectral estimation which fit into the low-rank signal model. We also investigate the effect of compression on the CRB by considering numerical examples of the DOA estimation scenario, and show how the CRB increases by increasing the compression or equivalently reducing the number of compressed samples.Comment: 14 pages, 1 figure, Submitted to IEEE Signal Processing Letters on December 201

The communicational properties of single photons explain their strange behavior in the double-slit experiment

Simultaneous observation of the wave-like and particle-like aspects of the photon in the double-slit experiment is unallowed. The underlying reason behind this limitation is not understood. In this paper, we explain this unique behavior by considering the communicational properties of the photons. Photons have three independently adjustable properties (energy, direction, and spin) that can be used to communicate messages. The double-slit experiment setup fixes two of these properties and confines the single photon’s capacity for conveying messages to no more than one message. With such a low communication capacity, information theory dictates that measurements associated only with one proposition can obtain consistent results, and a second measurement associated with an independent proposition must necessarily lead to randomness. In the double-slit example, these are the wave or particle properties of the photon. The interpretation we offer is based on the formalism of information theory and does not make use of Heisenberg’s uncertainty relation in any form

Too Interconnected To Fail: Financial Contagion and Systemic Risk In Network Model of CDS and Other Credit Enhancement Obligations of US Banks

Credit default swaps (CDS) which constitute up to 98% of credit derivatives have had a unique, endemic and pernicious role to play in the current financial crisis. However, there are few in depth empirical studies of the financial network interconnections among banks and between banks and nonbanks involved as CDS protection buyers and protection sellers. The ongoing problems related to technical insolvency of US commercial banks is not just confined to the so called legacy/toxic RMBS assets on balance sheets but also because of their credit risk exposures from SPVs (Special Purpose Vehicles) and the CDS markets. The dominance of a few big players in the chains of insurance and reinsurance for CDS credit risk mitigation for banks’ assets has led to the idea of “too interconnected to fail” resulting, as in the case of AIG, of having to maintain the fiction of non-failure in order to avert a credit event that can bring down the CDS pyramid and the financial system. This paper also includes a brief discussion of the complex system Agent-based Computational Economics (ACE) approach to financial network modeling for systemic risk assessment. Quantitative analysis is confined to the empirical reconstruction of the US CDS network based on the FDIC Q4 2008 data in order to conduct a series of stress tests that investigate the consequences of the fact that top 5 US banks account for 92% of the US bank activity in the $34 tn global gross notional value of CDS for Q4 2008 (see, BIS and DTCC). The May-Wigner stability condition for networks is considered for the hub like dominance of a few financial entities in the US CDS structures to understand the lack of robustness. We provide a Systemic Risk Ratio and an implementation of concentration risk in CDS settlement for major US banks in terms of the loss of aggregate core capital. We also compare our stress test results with those provided by SCAP (Supervisory Capital Assessment Program). Finally, in the context of the Basel II credit risk transfer and synthetic securitization framework, there is little evidence that the CDS market predicated on a system of offsets to minimize final settlement can provide the credit risk mitigation sought by banks for reference assets in the case of a significant credit event. The large negative externalities that arise from a lack of robustness of the CDS financial network from the demise of a big CDS seller undermines the justification in Basel II that banks be permitted to reduce capital on assets that have CDS guarantees. We recommend that the Basel II provision for capital reduction on bank assets that have CDS cover should be discontinued.Credit Default Swaps; Financial Networks; Systemic Risk; Agent BasedCredit Default Swaps, Financial Networks, Systemic Risk, Agent Based Models, Complex Systems, Stress Testing

Unidades de tradução adotadas na formação terminológica persa

Existem duas tendências para a formação terminológica persa. Na primeira, método conhecido como decalque, palavras são transformadas morfema por morfema. Assim, a Unidade de Tradução (UT) é um morfema. Na segunda, método conhecido como achado-equivalente conceitual, as definições de palavras são consideradas e a UT é uma palavra. O presente estudo foi desenhado para identificar qual das duas UT foi mais favorecida na formação terminológica persa. Para este fim, 40 prefixos em inglês foram estudados em 2324 palavras em inglês e em conjunto com seus equivalentes persas, aprovados pela Academy of Persian Language and Literature (APLL) como agência oficial de formação terminológica persa no Irã. Percebeu-se que o decalque era mais frequente, ou seja, morfemas eram mais frequentemente considerados UTs. Além disso, estratégias de tradução de prefixos foram introduzidas e examinadas em ambos os métodos. No método conceitual, prefixos foram ignorados, e não traduzidos morfema por morfema. No entanto, no decalque, prefixos do inglês foram traduzidos para prefixos do persa ou lexemas.Two trends exist for Persian term-formation. In the first method known as calquing, words are rendered morpheme by morpheme. Thus, the unit of translation (UT) is a morpheme. In the second method known as conceptual equivalent-finding, the definitions of words are considered and the UT is a word. The present study was designed to identify which of the two UTs was more favored in Persian term-formation. To this end, 40 English prefixes were studied in 2354 English words together with their Persian equivalents approved by the Academy of Persian Language and Literature (APLL) as the official term-formation agency in Iran. It was noticed that calquing was more frequent, i.e. morphemes were more frequently considered as UTs. Moreover, strategies of translating prefixes were introduced and examined in both methods. In conceptual method, prefixes were ignored and not translated morpheme by morpheme. However, in calquing, English prefixes were translated into Persian prefixes or lexemes

Language and Consciousness; How Language Implies Self-awareness

The relationship between language and consciousness has been debated since ancient times, but the details have never been fully articulated. Certainly, there are animals that possess the same essential auditory and vocal systems as humans, but acquiring language is seemingly uniquely human. In this essay, we investigate the relationship between language and consciousness by demonstrating how language usage implies the self-awareness of the user. We show that the self-awareness faculty encompasses the language faculty and how this self-awareness, that is uniquely human, enables us to create social realities through utilizing the social character of the language. We conclude that it is self-awareness that empowers humans to form collective intentionality and to structure societies. Establishing the relationship between self-awareness, language and society sheds light on connections between philosophy of mind, philosophy of language and philosophy of society